Question

Tommy Flanagan was telling you what he ate yesterday afternoon. He tells you, "I had either popcorn or raisins. Also, if I had cucumber sandwiches, then I had soda. But I didn’t drink soda or tea." Of course you know that Tommy is the worlds worst liar, and everything he says is false. What did Tommy eat? Justify your answer by writing all of Tommy’s statements using sentence variables (P, Q, R, S, T), taking their negations, and using these to deduce what Tommy actually ate.

Answer 1

tom ate sandwiches of cucumber and also had tea

Explanation:

The computation is shown below:

P:I = popcorn

Q:I = raisins

R:I = cucumber sandwiches

S:I = sodas

T:I = tea

1. It could be either popcorn or raisins

2. If i take sandwiches of cucumber so it also had soda

3. Do not drink soda or tea

Now considered the negation of 1, 2 and 3

So,

`\sim (PVQ) = \sim P \wedge \sim Q\\\\\sim (R \to S) = \sim(\sim R\vee S) = R \wedge \sim S\\\\ \sim(\sim S \vee \sim T) = S \wedge T`

Now combining 4, 5 and 6

We get

`\sim P \wedge \sim Q \wedge R \wedge \sim S \wedge S \wedge T\\\\\sim P \wedge \sim Q \wedge R \wedge T`

So, tom ate sandwiches of cucumber and also had tea