Thread: Negating implications

Hello all,

Please help me find the negation of the following:

1)If a>2 and b<-5, then |a|+ |b| >=7

So, I think this can be rewritten as A= a>2 and b<-5; B=|a|+ |b| >=7
and thus, a>2 and b<-5 and |a| + |b|<7

Though, I'm also confused cause it might be:

If a<2 and b>5 OR |a| + |b| >=7.....so as you guys can tell i'm throughly confused.


2) If the numbers a and b are primes, then the number a+b is composite.

Sort of having the same problem as above.

Thanks in advance.

Originally Posted by jusstjoe

Hello all,

Please help me find the negation of the following:

1)If a>2 and b<-5, then |a|+ |b| >=7

Couple of things to lay the ground work.

• 
• 
• 
• 

Your statement is of the form



You want to find,



Apply the rules above.

2) If the numbers a and b are primes, then the number a+b is composite.

Suppose , then a and b are odd.

For some then,





This implies,


Therefore a+b is even and not prime.

Now, if a or b is 2 then...this is not true. Consider the counter example with


then is prime (not composite)