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!