That's correct, they're not equivalent. There are two combinations on the left which evaluate as false, whereas there's only one combination on the right.
. I used the truth tables with heading as below
p q ~p ~p -> q p ∧ q
My last two columns were not the same, but in the mark scheme it says they are logically equivalent?
Those column headings don't make sense to me in relation to this question.
Do you have the question and your headings down correctly?
I got no it is not.. I used the truth tables with heading as below
p q ~p ~p -> q p ∧ q
My last two columns were not the same, but in the mark scheme it says they are logically equivalent?
You don't even need a truth table. p ∨ q means you have p or q. However p∧∼q means you have p and you don't have q. Clearly the latter says it is impossible to have q, where as the former says you may have q or p. Therefore they are not equivalent.
So while truth tables are useful to show working, I think you should practice working it out by pure reasoning as well.
That's correct, they're not equivalent. There are two combinations on the left which evaluate as false, whereas there's only one combination on the right.
Those column headings don't make sense to me in relation to this question.
Do you have the question and your headings down correctly?
You don't even need a truth table. p ∨ q means you have p or q. However p∧∼q means you have p and you don't have q. Clearly the latter says it is impossible to have q, where as the former says you may have q or p. Therefore they are not equivalent.
So while truth tables are useful to show working, I think you should practice working it out by pure reasoning as well.
This is the question the last part
This is the answer
So they are definitely not equivalent and the answer in the mark schemes is wrong?
So they are definitely not equivalent and the answer in the mark schemes is wrong?
I used truth tables and got that they are not.
What are you querying exactly?
p -> q is equivalent to ~p V q
So ~p -> q is equivalent to p V q which is the form originally given in the question. So as far as I can see, the answer (vi) is correct. (I haven't bothered eliminating all the other possibilities).
There is more than one that is logically equivalent.
That's fair enough - I was assuming the OP was disagreeing with the answer (vi) but as you said before he hasn't posted consistently what he's comparing!
So ~p -> q is equivalent to p V q which is the form originally given in the question. So as far as I can see, the answer (vi) is correct. (I haven't bothered eliminating all the other possibilities).
As I said, learn to do these quickly in your head using pure reasoning, then you'll never go wrong because you know the answer before you even draw the truth table.