QN1 by logical argument verify that {a} is not open for any real number "a".

i guess the set is not open since there is no open interval about "a"
instead the set is said to be closed since any of its complement must be open.
am i correct?

QN2 GIVE TWO COUNTER-EXAMPLES WHICH SHOWS THAT THE IMAGE OF INTERSECTION OF TWO SETS IS NOT EQUAL TO THE INTERSECTION OF THEIR IMAGES