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

Question

2. 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 (eg "pv q") to indicate the order of operations. (eg 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) Place parentheses a. IfI 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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