i cant understand the last example (example 3). So kindly explain in a better way..

 

 

Dear Student!

 ~(q or p) means complement(not or opposite) of (q or p). Now, (q or p): for each a∈R, a+0=a or 45 is not a multiple of 10, it means that q : for every a∈R, a+0=a or p: 45 is not a multiple of 10. As we have to find ~(p and q), so just find the complement of p, q and put 'and' connector between them. ~p means 45 is a multiple of 10(opposite of p). Similarly, ~q means there is at least one a for which a+0≠a(opposite or complement of earlier condition). So  ~(p and q):  45 is a multiple of 10 and there is at least one a for which a+0≠a.

Hope, you got it now!