TMUA DPiD Maths Mock Set 1 Paper 2 · Question 3

Let $A$ and $B$ be subsets of the $xy$ -plane, and consider the following statements.

$P$ : For all real numbers $x$ and $y$ , $(x,y)$ is in $A$ if and only if $(x,y)$ is in $B$ .

$Q$ : There exists a point $(x,y)$ that lies in both $A$ and $B$ .

Which of the following statements is true?

P

is necessary and sufficient for

Q

P

is necessary but not sufficient for

Q

P

is sufficient but not necessary for

Q

P

is not necessary and not sufficient for

Q

Q

is sufficient but not necessary for

P

P

and

Q

are logically equivalent.

Q

implies

P

whenever

A

is non-empty.

HBoth

P

and

Q

are always true.

examday