00:01
Hello, spins, here is our question that we have to see which of these are logically equivalent to p and a q.
00:14
So this is our truth table look like.
00:18
So now we just put the values first here we have true and true then false then false from q it's true false true false and negation of p means the opposite of p here we have true so here we get false then again here it's true it will be false it's false here we have true and here we have true and now negation of q it means the opposite if we have true then we the answer will be false it's forced then it's true here it's true and it's force it's force it will be true now first of all we will see for this one that it is equivalent to p and q or not so we find negation of p and we also find negation of q now we will find negation of p and negation of q so for negation of p and negation of q so for negation of p and negation of q uh false false is false false true is false true false is false and true true true is true now we have to see the opposite of negation of p and negation of q so now here we get true here we get true here we get true and here we get now we will see for p and q for p and q true true will be true true false is false true false is false and true false is false so this one negation into negation of p and negation of q is true true and false but the p and q is true force force so these both are not that's why negation of p into negation of sorry negation into negation of p and negation of q is not equivalent to p and q.
02:44
Now i will see for the second one, let me remove this.
03:03
The second one is that negation into p, then negation q.
03:11
So first of all we will find q then negation p.
03:17
So then means if the first statement is true, then the second statement have to be true if this first statement is true then the second statement is true or false it doesn't matter so uh q and q then negation of p here q is t true then negation of p is false it means true false false will be true true true true true true true will be true and the the then conditions here we have force so false true will be force now we have to see the negation of p then q negation into q then negation p so true means here we have false here we have false here we have force and here we have true now here we have false here we have true here we have force here we are false here we have force here we are force here we are false here we are true and here we are true again this one this statement is also not equivalent to p and a queue i will see for this third one for this we have to find negation of p then negation of q so negation of p then negation of q negation of p is false, then negation of q is false, it means it is true.
05:05
Negation of p is false, then negation of q is true.
05:10
It means the first statement is false, that is why it's false...