LOGIC

Logical operators

________ combine propositions to make other propositions, with the use of a truth- table you can determine whether the resulting pro position is true or false.

Quadrilateral ABCD

________ has equal sides therefore it is a square.

Illegal drugs

________ are dangerous to your well being.

prime number

A(n) ________ has only two factors.

Singular

________- the subject term denotes a(n) __single person /thing__.

Parallel lines

________ never intersect.A scalene triangle has no equal sides.

Formal fallacies

________- are invalid arguments due to flaw in logical structure** 2.

Biconditional

________:** Three points are collinear iff they lie on the same line.

Skin blemishes

________ are still present after 7 days of use.

Happiness

________ is the end of life.

incorrect argument

If the argument is a tautology, then it is considered valid; otherwise it is a** fallacy**/n** FALLACY-** A fallacy is a(n) ________ in logic which is a result of invalid reasoning.

right triangle

A(n) ________ has a right angle.

/ **SIMPLE PROPOSITION** * A proposition is declarative in nature  * It is a statement that needs affirmation or denial

maybe TRUE or FALSE (truth value) | **Affirmative Proposition**Canberra is the capital of Australia

**Universal

the subject term taken in __full extension__

** **Examples**

All Triangles are polygons                     No parallel lines meet at a point

**Particular

the subject term is taken only in __some extension__

** **Examples**

Most cats are afraid of water

**Singular

the subject term denotes a __single person/thing__

** **Examples**

A penguin is a bird

**Converse

** If you are out of cell phone load, then you cant send a text message

**Converse

** If 2 lines are perpendicular, then they intersect to form right angles

/n **State the converse of the following conditional statements

**  1

**Inverse

** If 2 lines intersect and didnt form right angles, then they are not perpendicular

/n **State the inverse of the following conditional statements

**  1

**Inverse

** If 2 lines intersect and didnt form right angles, then they are not perpendicular

**Contrapositive

** If 2 lines are not perpendicular, then they dont intersect to form right                          angles

/n **State the contrapositive of the following conditional statements

**  1

**Converse

** If three points lie on the same line, then they are collinear

**Biconditional

** Three points are collinear iff they lie on the same line

**    **Biconditional

** A number is divisible by 3 if and only if the sum of its digits is divisible by 3

[](https

/ lh6.googleusercontent.com/JGi_78UIyByHd9l-VKl06NRBfKjqb2Qv81Z3QJBjbcl5BKmDocc4KVxXpwkiy03q2BAMAfnFNu9RKPqSlqf8ViRVQT0e4BDKHik5f2SezzxNJBlc-16BqUh2kiz7KKsrq9v9v6qtPu7Xy1hmL7hPe9HjC6BJG_Y6g8aKREyTFRgE8L-eXxSOkHM7Bxf3OA) **HYPOTHETICAL OR CATEGORICAL

**Premise 2

**Textbooks are made of paper

**Premise 3

** Paper came from trees

**Premise 4

** Trees give Oxygen

**Conclusion

** Schools take away oxygen

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/ lh4.googleusercontent.com/TvD5s2_eBbLxxmCTfKDffuiTi_9tB2KdRWWr7tbJ_X6cEwjNaJDpRHchsxzT4M9jGFGSWfR2FxltwGQ4XXMs2ta7hUX21riNEbzOPNqdVewIA3NBtw-QZUgA_iD4c-f8FxdzeD_XReQZftzMq0jDeae2QHYzHRtHn5-b1_9WRw8zCCvvwBks6pvGvwT3rw) 1

**Minor Premise

contains the subject of the conclusion** 2

**Major Premise

contains the predicate of the solution

** /n /n /n /n /n /n **Example

**

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/ lh5.googleusercontent.com/d3EJV03FIs2QHBMzGdP5N5MsdlIxdl45a2Frw4CJBvoHCfzdpvYCwY9fOrDoNvSZl88kSv03TtcePO-r_qTLabDdnB5jrVhxfuPbrqP_xP-xzd-ygi-7eH9ZxRWQJxP7C0vSMcLxYwNinDfI3Mi2hzBp1nY0013Y47O6n9BBVMGMgIax9XT0gX2a9cJ6Qg) /n

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/ lh5.googleusercontent.com/hsbG5AbzXCcsW3l3QX8wu7XoHJKSv7DqNsdoS54o_RcFkdMyCTvMmn6lIuYp6HRNP_kzawVoBNJdZnWlG5E2N5O_-XuPiWIKnv3HZ8jI2-YpWZ5mneJHeusrMf8On5ljcPB_JU08y-xkVjNMNRt-_dE2LRZE_I-VEV4WRdNiAefashqumNmUoSqRJ7l57w) /n

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/ lh4.googleusercontent.com/QH1_ELroNV-_q_Bf2R-ClWa1eg7iyclG-J8G5RXm20BNgC90HjCRiN_uH3MBkAk2MRBTXHomtr_AuQsyL2Ws1YKYHLyDmCrJdk2XjLEnfsOBeQDPMTvQy-6A9NWUoNUmumrlx_MheihibWA4F1xZAFS9mRnb-FJTxtyr9wnd2ogMal4MyhxHsRfGitvT5g)

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/ lh5.googleusercontent.com/IJQZ8Xz-RqBmOsOWu7I9lxNy1vlYfKT8AriGXDeav7M3bOJNcgWRSTps9tbtAetbJ8UeKlb3_oQ-n393smnt2DkYlEZbHnII7VKuLwum2O_d3DD6GLSuJrAjBhSLx6U4oDvBqZDvyXBeZO4JpV_uUB1CoN7DOJEpta86DH-O0uj6R0QwoMoyatiFFc3Rkg)

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/ lh5.googleusercontent.com/U7UhJzpDgT-221mR07jTx-5BJ6adMF_R3P3wh9YzM9U4F0FiPlnPZ6OOLvwG62O0MOv4tI8w-2q-T9I5hlccXk8lix9XxMeRSWz9fX2ww7whAPI9rldJ82KUuZ9SNPz2uIkSOFK5OStGK_W9V5ewEmp6rJlYQR18k__dZEr8SsKBv9Ri6V9IX4hC3V5kOA) **OPERATIONS ON PROPOSITIONS**

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/ lh5.googleusercontent.com/eiFl7TnsMnWf7zDaq4mlBfBNA1V_cajd0W5CUm2YWqPTtavh9mm0svHgIP7Qhn4a6I4UZdb4CAvwrbX0ELEKp601wYJ0Ejah5MH3AutzZtVUmRJu53iHwQBfCegX7wXjy5hg2jeYs8M_8N2uZg2As42c2YVxcXTaxPqUnY6ozPHHFFrS_c3fyuk6ThAjBA) /n The fundamental elements of propositional logic are propositions statements that can be either true or false

/n **Example

**  1

**If 2 + 5 = 7 then (2) (5 )= 10** ***Solution***

  2 +5 = 7 which is a true statement, and q is the consequent (2)(5)= 10 which is also a true statement

**if 2 +5 = 7 then 2-5= 7**  ***Solution***

if p is the antecedent 2 + 5= 7 which is a true statement, and q is the consequent 2-5 = 7 which is a false statement, then the implication p  q "if 2 + 5 = 7 then 2-5= 7" is a false statement 3

**If 2 + 7 = 5 then 7 -5 = 2**  ***Solution***

if p is the antecedent 2 + 7= 5 which is a false statement, and q is the consequent 7-5 = 2 which is a true statement, then the implication p  q "if 2 + 7 = 5 then 7 -5=2" is a true statement  4

**if 2 + 7 = 5 then 2-5= 7**  ***Solution***

if p is the antecedent 2 + 7= 5 which is a false statement, and q is the consequent 2-5 =7 which is also a false statement, then the implication p  q "if 2 + 7 = 5 then 2 -5=7" is a true statement

**A square is a polygon if and only if the square is a rectangle**  ***Solution***

  If p is the proposition " A square is a polygon."

**A right triangle is a triangle if and only if the sum of the lengths of its sides is equal to the length of the hypotenuse**  ***Solution***

If p is the proposition "A right triangle is a triangle."

**The diagonals of a square are parallel if and only if the square is a quadrilateral**  ***Solution***

  If p is the proposition "The diagonals of a square are parallel" Which is a false statement a q is the proposition "the square is quadrilateral" which is a true statement, then the equivalence p⇔q "The diagonals of a square are parallel if and only if the square is a quadrilateral" is a false statement  8

**Parallel segments intersect at a point if and only if the segments have only one end point**  ***Solution***

  If p is the proposition "Parallel segment intersect at a point " Which is a false statement a q is the proposition "the segments have only one end point" which is a false statement, then the equivalence p⇔q " Parallel segments intersect at a point if and only if the segments have only one end point" is a true statement since both propositions are false stament /n /n **EQUIVALENCE -**  Simple sentence is true when the simple sentence is false and false when the simple sentence is true

/n **Example

**  1

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/ lh5.googleusercontent.com/AzqJCo1wr5DYugCB-8MXxjt8QdI-66IgN3ADpTNknpW-H9o5I4tnIq2qFguKcRF6tO93d1xwE_SEe7rZckyCEPK8y4myYT2iR9dWfuLPzfahYr2xFd7CRSCjhEmQBZYHo6wdzMXz4OCdzapeyCy72P1HRt2EkdatbbhXvAkevlc-1UQ1tjPMBf19qlTyIw) /n **ARGUMENT** * An assertion that a given set of statements called premises results in another statement called conclusions

**Formal fallacies

are invalid arguments due to flaw in logical structure** 2

**Informal fallacies

 are arguments whose premises adequately support the validity of its conclusion

**Example

**  | "Gods must exist, since every culture has some sort of belief in a higher being."

**Example

** "A measurement is a quantity that expresses the measure of an object being measured."

**Example

** All triangles are polygons

**Example

** A class of 40 was subjected to an informal survey about the mayoralty candidate they will support in the election

**Example

** Every school has a principal

**Example

** If Ralph was a UP student, then he would know the UPs official publication is The Collegian

/n **> FALLACY OF EQUIVOCATION** * committed when the ambiguity of a term or a phrase in an argument which has occurred at least twice is exploited of deliberately misused **Example

** The end of life is death

**Example

**  Every member of the gymnastic team is an outstanding dance sports performer

**Example

** Daniel failed most of his subjects in the 4th Grading Period because he did not submit his project in the 3rd Grading Period

/n **> AD VERCUNDIAM** * involves using a pronouncement of a person taken to be an authority but is not really one as evidence **Example

** Richard Dawkins, an evolutionary biologist and perhaps the foremost expert in the field, says that evolution is true

/n **> FALLACY OF FALSE DILEMMA** * limits unfairly an arguer to only two choices, as if the choice is on black or white **Example

** Decide

**Example

** Survey shows that mathematics in the most dislike subject

**Example

**  I believe in the resurrection of Jesus Christ

**Example

**  This soap will remove skin blemishes after 7 days of use

**Example

**  She is wrong when she claim that Girolamo Cardano was insane because she is only a Grade 10 student

Answer

Why not she