For A = {x|x is an integer greater than 7} and B = {x|x is an integer less than or equal to 12}, determine A∩B and A∪B.

A∩B =
{x|x is an integer greater than 7} and {x|x is an integer less than or equal to 12}=
{x|x is an integer greater than 7 and less than or equal to 12}


A∪B =
{x|x is an integer greater than 7} or {x|x is an integer less than or equal to 12}=
all integers

True or false: {16, 17, 18, 19}=[16,19] ?

False. The interval [16,19] contains all the number beginning at 16 and ending at 19 while the set {16, 17,  18, 19} only includes the four integers.

True or false: {16, 17, 18, 19} is a subset of (16,19) ?

False. The interval (16,19) does not include 16 and 19.

True or false: {16, 17, 18, 19} is a subset of [16,19] ?

True. The interval [16,19] contains all the numbers between and including 16 and 19.

indicates the sets to which the number belongs -144/4

This number belongs to an infinite number of sets, but if you mean "major" set of numbers, then -144/4 belongs to the negative rational numbers, and thus every set for which the negative rational numbers is a subset.

assume that power set of A equal to power set of B.then A=B.

This is not true: 
A= {1, 2} 
B= {4, t} 
have 

 

but 

 

(two sets are equal if they have exactly same elements) 

:)

- 144/4 to which set does the number belong

Your Answer:

this number is a fraction so it belongs to the rational numbers - this also means it belongs to the sets of numbers for which the rational numbers are a subset