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Types of Conditionals
Geometry
The converse of a conditional statement is formed by switching the hypothesis and conclusion.
p: x is prime.
q: x is odd.
Conditional: (p → q)
If x is prime, then x is odd.
Converse: (q → p)
If x is odd, then x is prime.
p q p → q q → p
T T
T F
F T
F F
T
F
T
T
T
T
F
T
Conditional Converse
The inverse of a conditional statement is formed by negating the hypothesis and conclusion.
p: x is prime.
q: x is odd.
Conditional: (p → q)
If x is prime, then x is odd.
Inverse: (~p → ~q)
If x is not prime, then x is not odd.
p q p → q ~p ~q ~p → ~q
T T
T F
F T
F F
T
F
T
T
F
F
T
T
F
T
F
T
T
T
F
T
Conditional Inverse
The contrapositive of a conditional statement is formed by performing the inverse and converse of the conditional statement.
p: x is prime.
q: x is odd.
Conditional: (p → q)
If x is prime, then x is odd.
Contrapositive: (~q → ~p)
If x is not odd, then x is not prime.
p q p → q ~q ~p ~q → ~p
T T
T F
F T
F F
T
F
T
T
F
T
F
T
F
F
T
T
T
F
T
T
A conditional and its contrapositive alwayshas the same truth value.
They are said to be logically equivalent.
conditional contrapositive
Write the converse, the inverse and the contrapositive for each conditional statement.
1) If the figure is a square, then it has four sides.
2) If I do not set my alarm, then I’ll be late to school.
Write the converse, the inverse and the contrapositive for each conditional statement.
1) If the figure is a square, then it has four sides.
Converse:If the figure has four sides, then it is a square.
Inverse:If the figure is not a square, then it does not have four sides.
Contrapositive:If the figure does not have four sides, then it is not a square.
Write the converse, the inverse and the contrapositive for each conditional statement.
2) If I do not set my alarm, then I’ll be late to school.
Converse:If I am late to school, then I did not set my alarm.
Inverse:If I set my alarm, then I will not be late to school.
Contrapositive:If I am not late to school, then I set my alarm.
HomeworkWorksheet:
Types of Conditionals #1
1.06
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