1-5 Conditional Statements

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Geometry & Trigonometry

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6 Terms

1
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Conditional Statement

If-then statement, includes a hypothesis after if and a conclusion after then

If p, then q; p —> q

<p>If-then statement, includes a hypothesis after if and a conclusion after then</p><p>If p, then q; p —&gt; q</p>
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Converse

Reverses the hypothesis and the conclusion of a conditional

If q, then p; q —> p

<p>Reverses the hypothesis and the conclusion of a conditional</p><p>If q, then p; q —&gt; p</p>
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Negation

Has the opposite meaning of the original statement; not p (~p)

<p>Has the opposite meaning of the original statement; not p (~p)</p>
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Inverse

Negate both the hypothesis & conclusion of the original statement.

If not p, then not q; ~p —> ~q

<p>Negate both the hypothesis &amp; conclusion of the original statement.</p><p>If not p, then not q; ~p —&gt; ~q</p>
5
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Contrapositive

Negate and reverse both the hypothesis & conclusion of a conditional

If not q, then not p; ~q —> ~p

<p>Negate and reverse both the hypothesis &amp; conclusion of a conditional</p><p>If not q, then not p; ~q —&gt; ~p</p>
6
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Biconditional statement

Combination of a conditional (p —> q) and it’s converse (q —> p)

p <—> q; p if and only if q

When p and q have the same truth value, the biconditional is true. When they have opposite truth values, it is false

<p>Combination of a conditional (p —&gt; q) and it’s converse (q —&gt; p)</p><p>p &lt;—&gt; q; p if and only if q</p><p>When p and q have the same truth value, the biconditional is true. When they have opposite truth values, it is false</p>

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