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Level 145

Logic Statements


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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