I'm having trouble with this problem can someone help

Question

A and B are sets of real numbers defined as follows. A={z l z ≤1} B={z l z <5} Write A∪B and A∩B using interval notation. If the set is empty, write ∅

Answer 1

A∪B is the union or combination of sets A and B.  Set A is all real numbers less than or equal to 1.  Set B is all real numbers less than 5.  Since 1 is less than 5, set B includes all real numbers less than 1; that is, set B already includes all of set A as a subset.  Hence, in interval notation:

 

A U B = B = (-∞,5)

 

A ∩ B in the intersection of sets A and B.  That is, it includes only those members that are contained in both set A and set B.  Since set A is a subset of set B, all of set A in contained in both sets A and B.  Hence, in interval notation:

 

A ∩ B = A = (-∞,1]