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conditional statement

if p, then q

conditional statement

p => q

p

hypothesis

q

conclusion

converse statement

if q, then p

converse statement

q => p

Biconditional Statement

p if and only if q

Biconditional Statement

p <=> q

Inverse statement

if ~p, then ~q

Inverse statement

~p => ~q

contrapositive statement

if ~q, then ~p

contrapositive statement

~q => ~p

two sides of a triangle are congruent

If two sides of a triangle are congruent, then the angles opposite the sides are congruent.

the angles opposite the sides are congruent

If two sides of a triangle are congruent, then the angles opposite the sides are congruent.

If the triangle is a right triangle, then the acute angles are complementary.

If the acute angles are complementary, then the triangle is a right angle.

If a triangle is equilateral, then it is equiangular.

A triangle is equilateral if and only if it is equiangular.

If a triangle is equilateral, then it is equiangular.

If a triangle is not equilateral, then it is not equiangular.

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

If two sides of a triangle are congruent, then the angles opposite the sides are congruent.

If a triangle is equilateral, then the measure of each angle of the triangle is 60°.

If the measure of each angle of a triangle is not 60°, then the triangle is not equilateral.

conditional statement

A statement that can be written in if-then form. (p -> q), where p is the hypothesis and q is the conclusion.

Converse

Switch the hypothesis and conclusion of the conditional

Inverse

Negate the hypothesis and the conclusion of the conditional

Contrapositive

Negate the hypothesis and the conclusion and switch the conditional

Biconditional

If the conditional and converse are true, you can combine them as a biconditional statement using the words if and only if. (p<->q)

Law of Detachment

If a conditional is true and its hypothesis is true, then its conclusion is true.

Law of Syllogism

If A then B. If B then C. If A then C.

conditional

an if-then statement

hypothesis

part following if

Conclusion

part following then

Converse

switches the hypothesis and the conclusion of a conditional

Biconditional

a statement in which the conditional and its converse are both true

Deductive Reasoning

reasoning that uses given statements and the rules of logic to reach a conclusion

Negation

has the opposite truth value of a statement

Inverse

negates both the hypothesis and the conclusion

Contrapositive

switches the hypothesis and the conclusion of a statement and negates both

equivalent statements

have the same truth value

Modus Ponens

If A, then B

Modus Tollens

If A, then B

Disjuntive Syllogism

A or B

Hypothetical Syllogism

If A, then B

Constructive Dilemma

A or B