Given: p: I will try out for the school play q: I will have a part in a play thi

Question

Given: p: I will try out for the school play q: I will have a part in a play this semester. Translate the following into symbolic logic expressions (e.g. “p v q”) Place parentheses to indicate the order of operations. (e.g. if you were placing parentheses to indicate the order of operations in an expression like 3 + 5* 2, you would do this: 3 + (5*2)

a. If I will try out for the school play then I will not have a part in a play this semester.

b. I am neither trying out for the school play nor will I have a part in a play this semester.

c. I will try out for the school play if and only if I will have a part in a play this semester.

d. I will try out for the school play or I will not try out for the school play but I will have a part in a play this semester.

e. If I will have a part in a play this semester then I will try out for the school play.

f. If I will try out for the school play and I will have a part in a play this semester then I will have a part in a play this semester or I will not try out for the school play.

Explanation / Answer

p: I will try out for the school play
q: I will have a part in a play this semester.

a. (p -> ~q)
If I will try out for the school play then I will not have a part in a play this semester.

b. ~p ~q
I am neither trying out for the school play nor will I have a part in a play this semester.

c. p <-> q
I will try out for the school play if and only if I will have a part in a play this semester.

d. (p v ~p) q
I will try out for the school play or I will not try out for the school play but I will have a part in a play this semester.

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