### Show if the following are logically equivalent I) P->Q and NQ ->Np II) N{P∆Q} AND...

Show if the following are logically equivalent
I) P->Q and NQ ->Np
II) N{P∆Q} AND {NP∆NQ}
2] Give A={7,8,4,5}
B={X, Y, Z}
I) What Type Of Mapping Is A TO B
II) state the D{F}
III) state the rang of R?

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With simple expressions like these, the easiest proof is to make a truth table...unless it is specifically prohibited in the question.

Also, there are precedence in the logical operators, just like + - * ÷.
see
http://en.wikipedia.org/wiki/Logical_connective

The ¬ operator (which I write as ~ for simplicity) has the highest priority, in this order.

Operator Precedence
¬ 1
∧ 2
∨ 3
→ 4
↔ 5

There the first expression is interpreted as (~p)∧q which is not an identity to p->~q.

However, writing the first expression as ~(p∧q) will give a truth table of
TT F
TF T
FT T
FF T
identical to that of
p->~q
TT F
TF T
FT T
FF T
hence the identity
~(p∧q) ≡ p->~q
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