Proposition Logic doubt

Question

Given: (p$ \vee$ q) is True. 

Find the truth value of statements, 

1. p is false or q is true. (Can't determine) 

2. If p is false then q is true. (True) 

is my answer correct????? 

Comments

(P $\vee$ Q)  is True that's mean atleast one is True.

or we can say,

P is True or Q is True or both are True.

on the basis of this information, can we determine truth value of given statements in question?

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No. As I already said that we don’t know the truth values of $P$ and $Q$ it means we can’t determine the truth value of your statement 1. You might have to define like “who is Jack/Jill” and “what exam it was” etc otherwise it is difficult to know the truth values of P and Q.

If P and Q are mathematical expressions like $1+1=2$(in decimal number system) then it is easy to determine the truth values but here it is difficult to know the truth values for P and Q.

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I already defined meaning of p and q in comment. 

https://gateoverflow.in/403660/proposition-logic-doubt?show=403784#c403784

p: Jack is pass.

q:Jill is pass

Answer 1

The statement "If (p ∧ q) is True, then if p is false then q is true" is true.

We know that (p ∧ q) is true, which means that both p and q are true. If p were false, then (p ∧ q) would be false, which contradicts our initial assumption. Therefore, we can conclude that p must be true.

Now, if p is true, then the conditional statement "if p is false then q is true" is vacuously true, since the antecedent (p is false) is false.

Therefore, the statement "If (p ∧ q) is True, then if p is false then q is true" is true.

The first statement, "p is false and q is true," cannot be determined from the fact that (p ∧ q) is true, since there are other possibilities for p and q to be true simultaneously.