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Chapter 6: Q20. (page 212)

Write the contrapositive of the converse of the inverse of the conditional: if r, then s.

Short Answer

Expert verified

The contrapositive of the converse of the inverse of given conditional statement is if s then r.

Step by step solution

01

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

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

If the given statement is ‘’If p then q’’, the converse is ‘’If q then p’’.

If the given statement is ‘’If p then q’’, the inverse is ‘’If not p then not q’’.

02

Step 2. Define inverse and converse of the given conditional

The given conditional statement is r→sor if r then s.

Then define inverse statement for conditional:

Inverse statement of r→sis ~r→~sor if not r then not s

Define converse of the conditional:

The converse of the statement ~r→~sis~s→~r or if not s then not r.

03

Step 3. Check the converse of the inverse of conditional

From the definition of contrapositive, define contrapositive of the converse of the inverse of the given conditional statement iss→r or if s then r.

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