Question

consider the given statement:If we are having sushi for dinner, then it is not Sunday.For each statement below, determine if it is equivalent to the given statement, the negation of the the given statement, or neither of these.

Answer 1

The given statement is:

If we are having sushi for dinner, then it is not Sunday.

The statements are:

p: We are having sushi

q: It is not sunday

The statement is given by:

`p\rightarrow q=neg\text{ p}\lor q`

Negation of p or q.

The statement "We are having sushi for dinner and its sunday" is:

`p\wedge neg\text{ q}`

Option A is negation of the given statement.

The stetement "If we are not having sushi for dinner, then it is Sunday." is:

`\text{neg p}\rightarrow negq`

Option B is neither.

The statement "It is not Sunday and we are not having sushi for dinner" is given by:

`q\wedge\text{ neg p}`

Option C is neither.

The statement If its Sunday, we are not having sushi for dinner is given by:

`p\rightarrow q`

So option D is equivalent to the statement.