Question

Consider the following statements:

P: Good mobile phones are not cheap
Q: Cheap mobile phones are not good
L: P implies Q
M: Q implies P
N: P is equivalent to Q

Which one of the following about L,M, and N is CORRECT?

• A. Only L is TRUE
• B. Only M is TRUE
• C. Only N is TRUE
• D. L,M, and N are TRUE.

Answer 1

The correct option is D L,M, and N are TRUE.

g : mobile is good
c: mobile is cheap
P: Good mobile phones are not cheap
$g\to c{}^{\prime }\equiv (g{}^{\prime }+c{}^{\prime }$)
Q: Cheap moblie phones are not good
$c\to g{}^{\prime }\equiv (c{}^{\prime }+g{}^{\prime }$)
$\therefore$ Both P and Q are equivalent.
L : $P\to Q$
M : $Q\to P$
N: P $\equiv Q$
Since both P and Q are equivalent, all three of L,M, N are true.
So correct option is (d).