Consider the following statements. i. If D is dog, then D is very good. ii. If D is very good, then D is dog.

QUESTION

Miscellaneous Exercise 1 | Q 4.19 | Page 33

Consider the following statements.
i. If D is dog, then D is very good.
ii. If D is very good, then D is dog.
iii. If D is not very good, then D is not a dog.
iv. If D is not a dog, then D is not very good. Identify the pairs of statements having the same meaning. Justify.

SOLUTION

Let p : D is dog.
q : D is very good.
Then the given statement in the symbolic form is i. p → q
ii. q → p
iii. ~q → ~p
iv. ~p → ~q

Since a statement and its contrapositive are equivalent, statements (i) and (iii) have the same meaning.
Since converse and inverse of a compound statement are equivalent, statements (ii) and (iv) have same meaning.