Mathematics: If A={1,2,3,4,5},AnB={3,4,5}and sub={1,2,3,4,5,6},find the set B

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If A={1,2,3,4,5},AnB={3,4,5}and sub={1,2,3,4,5,6},find - id1234534512345610242383, iiisavageoreo

chaseashley24

16.03.2022

$B = \{3,4,5,6\}$

Step-by-step explanation:

Given

$A = \{1,2,3,4,5\}$

$A\ n\ B = \{3,4,5\}$

$A\ u\ B = \{1,2,3,4,5,6\}$

Required

Find set B

$A\ n\ B = \{3,4,5\}$ means that the common elements in A and B are 3, 4 and 5.

This implies that:

A subset of B are:

$x = \{3,4,5\}$

And it also means that $\{1,2\}$ are not elements of B.

The remaining elements (y) of B are then calculated as follows:

$y = (A\ u\ B) - (\{1,2\}\ u\ x)$

This gives:

$y = \{1,2,3,4,5,6\} - (\{1,2\} u \{3,4,5\})$

$y = \{1,2,3,4,5,6\} - \{1,2,3,4,5\}$

Remove common elements

$y = \{6\}$

Hence, the set B is:

$B = \{\{x\},\{y\}\}$

$B = \{3,4,5,6\}$

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