Question

Find the smallest set A such that AU{4, 5} = {1,2,3,4,5)

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Answer 1

The smallest set A = { 1 , 2 , 3 }

Given :

A ∪ { 4 , 5 } = { 1 , 2 , 3 , 4 , 5 }

To find :

The smallest set A

Solution :

Step 1 of 2 :

Define union of two sets

For two given sets A and B the union of two sets is denoted by A ∪ B and defined as

A ∪ B = { x : x ∈ A ∨ x ∈ B }

Step 2 of 2 :

Find the smallest set A

Here it is given that for the set A

A ∪ { 4 , 5 } = { 1 , 2 , 3 , 4 , 5 }

Thus we have A = { 1 , 2 , 3 }

Such that { 1 , 2 , 3 } ∪ { 4 , 5 } = { 1 , 2 , 3 , 4 , 5 }

Hence the smallest set A = { 1 , 2 , 3 }

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