Determine the negation of the expression

[ur5pointos2sl]

The question states:

Determine the negation of the expression.

p -> q ^ r.

I am having difficulty finding the negation. Below are the steps I have taken in an attempt to come to the solution.

The - symbol will be the negate symbol.

p -> q ^ r

(-p OR q) ^ r

-(-p OR q) ^ r

(p ^ -q) ^ r

-((p ^ -q) ^ r)

-p OR - r OR q

-(p ^ r) OR q

I feel like I am going in circles. I have made truth tables to compare but have had no luck. Please any advise would be appreciated.

 

[ironspud]

If you look at a truth table for a conditional statement such as P\rightarrow Q, you should find that the only time this statement is rendered false is if the antecedent (the first part, P) is true and the consequent (the second part, Q) is false.

So, what does that tell you about your problem? Keep the antecedent as it is, and negate the consequent, (Q\wedge R).

 

[ur5pointos2sl]

If you look at a truth table for a conditional statement such as P\rightarrow Q, you should find that the only time this statement is rendered false is if the antecedent (the first part, P) is true and the consequent (the second part, Q) is false.

So, what does that tell you about your problem? Keep the antecedent as it is, and negate the consequent, (Q\wedge R).

Thank you!