CH2-Logical Operators

What is the contrapositive of the implication A+ → new car?

• A+ only if new car

• If no new car, then no A+

• New car is necessary for A+

• No A+ means no new car

Answer explanation

The contrapositive of A+ → new car is 'If no new car, then no A+' which is the correct choice.

Which of the following statements is equivalent to 'p is sufficient for q'?

• q is necessary for p

• p only if q

• p if and only if q

• q if p

Answer explanation

The statement 'p if and only if q' is equivalent to 'p is sufficient for q'.

What is the real-world scenario for the inverse of the implication if Louay helps Lina with her homework, then Lina's grades improve?

• If Louay doesn't help Lina with her homework, then Lina's grades won't improve.

• If Louay helps Lina with her homework, then Lina's grades improve.

• If Lina's grades improve, then Louay helped her with her homework.

• If Lina's grades improve, then Louay didn't help her with her homework.

Answer explanation

The inverse of p → q is ¬p → ¬q, where the negation of both the antecedent and consequent are taken to get the inverse statement.

Which of the following is equivalent to the converse of Nour → new car?

• ¬q → q

• q → ¬p

• ¬p → q

• ¬q → ¬p

Answer explanation

The converse of A+ → new car is ¬new car → A+. Therefore, the equivalent statement is ¬p → q.

What is the contrapositive of the statement '¬q → q'?

• q → ¬q

• q → q

• ¬q → ¬q

• ¬q → q

Answer explanation

The contrapositive of '¬q → q' is '¬q → q', which is the correct choice.