Question

P=(2;3;5;7;11)does prime numbers set satisfy closure property under addition in mathematics

Answer 1

Given:

P=(2,3,5,7,11)

To find:

satisfy closure property by addition and find a given set is prime number set.

Solution:

formula:

according to closure property of addition: a+b =c

where a and b is the whole number and their addition will be a whole number.

P=(2,3,5,7,11)

simply the above-given set contains only prime numbers to check it the given condition we apply the closure property of addition.

In given set p, we assume:

2,3,5 is equal to a, b,c then apply the closure property:

⇒2+3=5

⇒5=5

then we take 3,5, and 7 as a,b, and c then

⇒3+5=8

⇒8 ≠7  

similarly, In  5,7, and 11:

⇒5+7= 12

⇒12 ≠ 11

that's why we can say that the above given prime number set doesn't satisfy closure property.