Question

Logic Quiz 5 Show these two compound propositions to be true or false 1. Rome is the capital of Italy or Paris is the capital of England 2. If London is not the capital of Italy then Stockholm is the capital of Italy 3. 4. Given that A, B, C, are true statements and X, Y, Z are false, show that the following two statements (a and b) are true or false (Xv Y)AXvZ) a) b) I(B C)v (CAB) Prove and explain the following two deductions: 8.a 1. AAB 8.b 1. 2. J Prove and explain the following four arguments 2 K 2 M 10.b 10.a 1. P^R 2. (P > Q)(R> S) 1. C>D 2. B>C 3. A>B 4. AvE 5.D 5, Explain and give an example of an Implications, th of an ‘ if-then statement 6. Explain / show why if A' and B' are both true, then 'A v B' is 7. Explain / show why if both 'A' and 'B' are both true and Z is false, then A, (B v Z)' is true

Answer 1

1) In an or statement, if any one of the sub-statements is true, then the statement is true.

As "Rome is capital of Italy" is true, the given statement is true

2) London is not the capital of Italy is true. Stockhold is the capital of Italy is False

T=>F is False. So the given statement is False

3) X or Y is F or F which is F and X or Z is F or F which is F

So (X or Y) and (X or Z) = F and F = False

(B and C) = T and T = T, C and B = T and T = T

And ~ (C and B)= ~ T=F

So (B ^ C) or ~(C ^ B) = T or F=T

Which means ~[ (B ^ C) or ~(C ^ B)]=~T=F

4) A ^ B means both A and B are true. In particular, A must be true. So this argument is correct

I, J are both given to be true. I and J is true when both I and J are true (which is given)

So I and J is a true statement