Derived Forms of a Conditional Statement
There are three ways to restate a conditional statement – the converse, the inverse, and
the contrapositive. However, restating the statement into one of these forms may change the
meaning of the original statement. The conditional statement, p ⟶ q, may be restated in the
following forms:
Converse Form : q ⟶ p
Inverse Form : ∼ p ⟶ ∼ q
Contrapositive Form : ∼q ⟶ ∼ p
Example 5
Write the converse, inverse and contrapositive of the given sentence.
“If Alegria will study her lessons, then she will pass the test”.
Solutions:
p ⟶ q : “If Alegria will study her lessons, then she will pass the test”.
Converse : If Alegria will pass the test, then she will study her lessons.
Inverse : If Alegria will not study her lessons, then she will not pass the test.
Contrapositive: If Alegria will not pass the test, then she will not study her lessons.
Example 6
Write the converse, inverse and contrapositive of the given sentence.
If two triangles are congruent, then the two triangles are similar.
Solution:
p ⟶ q: If two triangles are congruent, then the two triangles are similar.
Converse : If two triangles are similar, then the two triangles are congruent.
Inverse : If two triangles are not congruent, then the two triangles are not similar.
Contrapositive: If two triangles are not similar, then the two triangles are not congruent.