Question

1.6. Let A = { x:x is a positive prime less than 15} and B = {x:xeN and
0< x-3<10), then find
AUB
ii) AnB
Also represent it in Venn diagram

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Answer 1

Given :-

◉ $\quad$ A = { x : x is a positive prime < 15 }

◉ $\quad$ B = { x : x ∈ N ; 0 < x - 3 < 10 }

To Find :-

◉$\quad$ A ∪ B

◉ $\quad$A ⋂ B

Solution :-

Venn Diagram :-

$\setlength{ \unitlength}{1.7cm} \thicklines \begin{picture}(10,10) \put(0,0){ \circle{2}} \put(0.5,0){ \circle{2}} \put( - 0.1, - 0.7){ \sf A} \put(0.5, - 0.7){ \sf B} \put(0.25,0){ \vector(1,0){1.2}} \put(0.25,0){ \circle{0.02}} \put(1.5,0){ \sf A \cap B } \end{picture}$

i)

Union Operation on Sets :-

Union combines the elements of two sets in one set, with no duplicate values.

So,

A = { 2, 3, 5, 7, 11, 13 }

B = { 4, 5, 6, 7, 8, 9, 10, 11, 12 }

⇒$\quad$ A ∪ B = { 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11 ,12 , 13 }

ii)

Intersection operation on Sets :-

It results in a set of elements which belong to both the sets. Or are common in both sets.

So,

A = { 2, 3, 5, 7, 11, 13 }

A = { 2, 3, 5, 7, 11, 13 } B = { 4, 5, 6, 7, 8, 9, 10, 11, 12 }

⇒$\quad$ A ⋂ B = { 5, 7, 11 }

Answer 2

I can't solve it please telll!