Question

Could someone help me with this problem?
Use the appropriate De Morgan law to negate the following conditional: (P -> Q) -> (R -> T)

Answer 1

Note: Simplify the resulting statement by applying the rule wherever possible. In other words, your final answer should only have negations of simple propositions.

Answer 2

This should help:

A->B = 'A V B

Answer 3

I know the equivalent but I am not sure how to apply in to the big picture since it is smaller conditionals within a larger one.

Answer 4

Break P->Q into 'P V Q and R-T into 'R V T

Answer 5

Right but I need to negate the whole thing as well as the smaller pieces

Answer 6

What?

Answer 7

(P->Q) -> (R->T) = ('P V Q) -> ('R V T)

Answer 8

is ' the negation?

Answer 9

Yes.

Answer 10

That would be the complete answer?

Answer 11

No. There's another implication.

Answer 12

Take a guess at what we do with it? The same exact thing.

Answer 13

That is where I am stuck at.

Answer 14

Well, simply negate the expression ('P V Q) = '('P V Q)

The implication turns to an "or", just like before. And ('R V T) remains unchanged.

Answer 15

Pretend the expressions are just variables, like A, or B, or C or whatever...

Answer 16

See?

Answer 17

Uh, no. I'm not really seeing it...

Answer 18

Alright, let me draw.