Write the converse, inverse, contrapositive of the following statement. If 2 + 5 = 10, then 4 + 10 = 20.

QUESTION

Miscellaneous Exercise 1 | Q 4.15 | Page 33

Write the converse, inverse, contrapositive of the following statement.

If 2 + 5 = 10, then 4 + 10 = 20.

SOLUTION

Let p : 2 + 5 = 10
q : 4 + 10 = 20

∴ The given statement is p → q.

Its converse is q → p.
If 4 + 10 = 20, then 2 + 5 = 10

Its inverse is ~p → ~q.
If 2 + 5 ≠ 10 then 4 + 10 ≠ 20.

Its contrapositive is ~q → ~p.
If 4 + 10 ≠ 20 then 2 + 5 ≠ 10.