Question

Suppose that U is the set defined as U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } . Find the sets A and B defined as follows. A = { x ∈ U ∣ x>5 and x>7 } = { } B = { x ∈ U ∣ x>5 or x>7 } =

Answer 1

Explanation:

Given that U is the set defined as

U ={1,2,3,4,5,6,7,8,9,10}

A = { x ∈ U ∣ x>5 and x>7 }

i.e. x is the set of natural numbers which are upto 10 and greater than both 5 and 7. this is equivalent to numbers greater than 7 and less than or equal to 10

So A =
`A={(8,9,10)}`

The set B is such that B contains all elements from U which are either greater than 5 or greater than 7

This is equivalent to all numbers in U which are greater than 5

So

`B=(6,7,8,9,10)`