Answer to Question #167541 in Discrete Mathematics for Eric

Question

1. If the truth value of P ⊕ Q in 2^3 is 0 0 1 1 1 1 0 0 then what is P <=> Q ins 2^3?
2. If the truth value for P v Q (P or Q) in 2^3 is: 1 1 1 1 1 1 0 0 then what is the truth value for P => Q in 2^3?
3. List all the Premises and Conclusion in the following argument: Either Alfred or Bill (or both) will go to the party. If Bill goes and Claire does not then Dinah will go. Claire will go if Alfred does not go. Therefore Dinah will go.
4. List all the Propositions in the following argument: Either Alfred or Bill (or both) will go to the party. If Bill goes and Claire does not then Dinah will go. Claire will go if Alfred does not go. Therefore Dinah will go.
5. Translate the logical expression into English. P: Today is Thursday. Q: Tomorrow is Saturday. R: I will get paid. ~(P ∧ Q) => ~ R

Answer 1

1.From truth tables:

if $P\oplus Q$ is true then $P\iff Q$ is false, and vice versa.

So, truth value of $P\iff Q$ is: 11000011

2.Using truth tables and results of question(1), we get:

truth value for $P\implies Q$ : 11 1(0)1(0)1(0)1(0) 11 (positions 3,4,5,6 can be 0 or 1)

3.Premises:

• Either Alfred or Bill (or both) will go to the party
• If Bill goes and Claire does not then Dinah will go
• Claire will go if Alfred does not go

Conclusion:

• Dinah will go

4.

• Alfred will go to the party
• Bill will go to the party
• Claire will go to the party
• Dinah will go to the party

5.If today is not Thursday and tomorrow is not Saturday, then I will not get paid.