2.3 disjunction, conjuction, and negation

2.3 disjunction, conjuction, and negation

Negation on an operation on a proposition means that you’re denying the proposition

In propositional logic we focus on 4 kinds of propostional logic which are…

conditionals (Has the “if, then” logic)

Conjunction (has the “and” function

disjunction (has the “or” function)

negation (has the “not-” function)

2 negations cancel each other out ( negation + not-t = t)

The truth condition for a negation is that the thing negated is false. If “I am tall” is false, then not-t is true

if the proposition is false, the negation is true, if the proposition is true, the negation is false

Conjunctions are propositions which assert the truth of two separate propositions (ex. on other side)

“He is a lawyer and a doctor” (l and d). This is only true if both conjuncts(the two propositions on either side of the “and”) are true. Otherwise, it’s false.

if p is true, and q is true, p and q are both true

if p is true, and q is false, p and q are false

if p is false, and q is true, p and q are false

is p is false, and q is false, p and q are false

this is for conjuncts (and)

A disjunction asserts that at least one of two propositions is true.

“I’ve seen her in my office, she is either a lawyer or an accountant.” If one or more of the disjuncts(the two propositions on either side of the “or”) is true, then the whole thing is true

if p is true, q is true, p or q is true

if p is t, q is false, p or q is true

if p is false, q is true, p or q is true

if p is false, q is false, p or q is false

this is for disjuncts (if one or more is true, the whole thing is true)

Notice that in normal English, we may use “or” in inclusive or exclusive ways….

Inclusive = both disjuncts can be true at the same time. (You allow many things to occur) You can have both and still be right

Exclusive = only one of the two disjuncts can be true at the same time (you’re restrictive of things) either one of the other, cannot be both

P or q, Not-p, therefore q, is called….

VALID disjunctive syllogisms (she is in the classroom or her office. She is not in the classroom, so she is in her office) 2 premises have to be true

P or q, not q, therefore p. This is INVALID

this is invalid because only one disjunct can be true at the same time, and this is the EXCLUSIVE use of “or”