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An advertisement for a tennis magazine states, "If I'm not playing tennis, I'm watching tennis. And If I'm not watching tennis, I'm reading about tennis." We can assume that the speaker can do at most one of these activities at a time. What is the speaker doing?

  1. Playing tennis
  2. Watching tennis
  3. Reading about tennis
  4. None of the above
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Let, $T_{p}$ be "The speaker is playing tennis"

, $T_{w}$ be "The speaker is watching tennis"

, $T_{r}$ be "The speaker is reading about tennis"

Then the advertisement for a tennis magazine states,

$(\overline{T_{p}} \rightarrow T_{w} ) \wedge \left ( \overline{T_{w}} \rightarrow T_{r} \right )$

 We need to assume that the speaker can do at most one of these activities at a time.

We can do this by choosing

$T_{w}$ =  $T$

$T_{p}$ =  $F$

 $T_{r}$ =  $F$

$\Rightarrow$$(\overline{T_{p}} \rightarrow T_{w} ) \wedge \left ( \overline{T_{w}} \rightarrow T_{r} \right )$

$\Rightarrow$$(\overline{F} \rightarrow T ) \wedge \left ( \overline{T} \rightarrow F \right )$

$\Rightarrow$$(T \rightarrow T ) \wedge \left ( F\rightarrow F \right )$

$\Rightarrow$$( T ) \wedge \left ( T\right )$

$\Rightarrow$  $T$

Hence the answer is B) Watching tennis

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