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# some logic help :) watch

1. Hey, I've ben attempting some D2 (a bit unsucessfully, I say ashamedly), and I stumbled across this question which I can make neither head nor tail of (even with the answer)

the question is (for those of you with books, MEI D2/C Ex. 4E Q.7)

Express the proposition using only , ~ and

Apparently the answer is ~ ~ . Can someone please explain to me how this is equivalent?

EDIT: I've just drawn up a truth table, and I can see why this is equivalent (well, I can see that it IS equivalent, but I don't understand WHY this is the case?). And how would I get from the first one to the second one?
2. Using my Logic taught in Computing.

If is false, then the statement is always true (False AND something is always false, and the negation of False is true - thus the statement is true).
If is true, then you have two cases:
is true, in which case ~ is false and the entire thing evaluates to true.
is false, in which case the entire thing is false.

This should agree with the definition of 'implies' (that, is always true, and is ).

I hope this helps.
3. (Original post by foolsihboy)
Hey, I've ben attempting some D2 (a bit unsucessfully, I say ashamedly), and I stumbled across this question which I can make neither head nor tail of (even with the answer)

the question is (for those of you with books, MEI D2/C Ex. 4E Q.7)

Express the proposition using only , ~ and

Apparently the answer is ~ ~ . Can someone please explain to me how this is equivalent?

EDIT: I've just drawn up a truth table, and I can see why this is equivalent (well, I can see that it IS equivalent, but I don't understand WHY this is the case?). And how would I get from the first one to the second one?
If you consider, when is ever false? There is only one combination of truth values for p,q where this is the case.

Then you just negate it to find when is true.

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