Question

A and B are sets of real numbers defined as follows.A= {z│z > 4}B= {z│z ≤ 9}Write A U B and A ∩ B using interval notation. If the set is empty, write Ø

Answer 1

`AnB=(5,6,7,8,9)`

`(AUB)=(5,\infty) U (-\infty,9)`

Explanation:

From the question we are told that

A= {z│z > 4}

B= {z│z ≤ 9}

Generally A&B are assumed to be really integers

therefore

A={5,6,7,8,.....}={z│z > 4}

B=(9,8,7,6.....)={z│z ≤ 9}

a)For
`AnB`

Mathematically the
`AnB` is given as

`AnB`=
`A=(5,6,7,8,9,10......) n B=(9,8,7,6,5,4,3,2,1......)`

`AnB`=(5,6,7,8,9)

Therefore the intercept
`AnB` is Given as

`AnB=(5,6,7,8,9)`

b) for
`AuB`

Mathematically the
`AuB` is given as

`AuB`=
`A=(5,6,7,8,9,10......) U B=(9,8,7,6,5,4,3,2,1......)`

`AuB`=
`(5,\infty) U (-\infty,9)`

Therefore the union
`AuB` i given as

`AuB`=
`(5,\infty) U (-\infty,9)`