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## Question:Are sets A = {1, 2, 3, 4} ,B = {x : x ∈ N and 5 ≤ x ≤ 7} disjoint? Why?

Posted by: Avadhoot Shinde on: 24 May, 2023

The elements of set A are 1. 2. 3 and 4.

Now, the elements of set B as per given conditions are 5, 6 and 7.

So, there are no common elements in the two sets A and B, i.e. there is no intersection between sets A and B.

Hence, the sets A and B are disjoint sets.

Sets A and B are disjoint because their intersection is empty.

Here A=1,2,3,4 and B=5,6,7

There is no common elements found

So sets A and B are disjoints

Draw rectangle. Randomly put 10 points, name them as 1,2,3etc. Now put a circle around 1,2,3,4. put another circle around 5,6,7. If the circle intersect and contains any common number to both the circle. A ,B are not disjoint otherwise disjoint .
Two sets A & B are called Disjoint Sets iff they have no common element. Here, A={1,2,3,4} and B ={5,6,7}. B is in roster form here. Now ,A and B have no common element, so they are called Disjoint Sets.

N : Denotes NATURAL NUMBERS .

B - Natural numbers between 5 and 7

i.e, B={5,6,7}

so ,each element of A and B are different ....hence, these are DISJOINT SETS.

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