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Chapter 6: Q19. (page 212)

What simpler name can be used for the converse of the inverse of a conditional?

Short Answer

Expert verified

The converse of the inverse of a conditional statement is Contrapositive.

Step by step solution

01

Step 1. Define contrapositive, inverse, and converse for the given statement

If the given statement is 鈥樷�橧f p then q鈥欌��, the contrapositive is 鈥樷�橧f not q then not p鈥欌赌�.

If the given statement is 鈥樷�橧f p then q鈥欌��, the converse is 鈥樷�橧f q then p鈥欌赌�.

If the given statement is 鈥樷�橧f p then q鈥欌��, the inverse is 鈥樷�橧f not p then not q鈥欌赌�.

02

Step 2. Let a conditional

Consider conditional statement is p鈫�q.

Then define inverse statement for conditional:

Inverse statement of p鈫�qis ~p鈫�~q
.

Define converse of the conditional:

The converse of the statement ~p鈫�~qis ~q鈫�~p.

03

Step 3. Check the converse of the inverse of conditional

From the definition of contrapositive, define contrapositive of conditional as:~q鈫�~p

Hence, the converse of the inverse of a conditional statement is Contrapositive.

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