Question

Given the pair of statements:

K ⊃ ∼ (E • R) and (E • K) ⊃ ∼ R
These statements are:
a.Logically equivalent.
b.Contradictory.
c.Consistent.
d.Invalid.
e.Inconsistent.

Answer 1

The pair of statements K ⊃ ¬ (E • R) and (E • K) ⊃ ¬ R are consistent because they can be true at the same time without contradicting each other.option a).Logically equivalent.

Step-by-step explanation:

The student has asked whether the pair of statements K ⊃ ¬ (E • R) and (E • K) ⊃ ¬ R are logically equivalent, contradictory, consistent, invalid, or inconsistent. To assess this, let's break down each statement:

• The first statement K ⊃ ¬ (E • R) means 'If K, then not (E and R)'
• The second statement (E • K) ⊃ ¬ R means 'If E and K, then not R'

By examining these statements, we can see that the pair is consistent. If K leads to the negation of (E and R), it is possible for E and K to also lead to the negation of R, as the first statement implies that K cannot coexist with both E and R simultaneously. Thus, there is no contradiction. However, they are not logically equivalent because one cannot be directly inferred from the other without additional information.