Question

"If $x$ is a member of set $S$, then $x$ is not a member of set $T$," is logically equivalent to which of the following?
I. If $x$ is a member of set $T,$ then $x$ is not a member of set $S$.
II. If $x$ is not a member of set $T,$ then $x$ is a member of set $S$.
III. If $x$ is not a member of set $S,$ then $x$ is a member of set $T$.

• A. I only
• B. II only
• C. III only
• D. I and II
• E. None of the above

Answer 1

The correct option is A I only

If $x$ is a member of set $S$, then $x$ is not a member of set $T$ i.e.

If $S=\left\{x\right\}$, Then, $T\ne \left\{x\right\}$

Obviously, if $x$ is a member of set $T$, then $x$ is not a member of set $S$ i.e. if $T=\left\{x\right\}$, then $S\ne \left\{x\right\}$ is equivalent to the above statement.