Ans:- A set A is said to be a subset of a set B, if every element of A is also an element of B. In other words, A⊂B if whenever a∈A, then a∈B. It is often convenient to use the symbol ⇒ which means "implies".
For A to be a subset of B, all that is needed is that every element of A is in B. It is possible that every element of B may or may not be in A. If it so happens that every element of B is also in A, then we shall also say that B ⊂ A. In this case, A and B ate the same sets, so that we have A ⊂ B and B ⊂ A ⇔ A = B, where ⇔ is a symbol for two way implications and is usually read as “if and only if” and briefly written as “iff”
Every set A is a subset of itself, i.e., A ⊂ A. An empty set has no elements. So, a null set is a subset of every set. Let the set Q of rational numbers is a subset of the set R of real numbers and so, we could write Q ⊂ R.
If A is the set of all divisors of 56 and B is the set of all prime divisor of 56, then B is a subset of A and we write B ⊂ A. Let A = {1, 3, 5 } and B = {x : x is an odd natural number less than 6}. Then, A ⊂ B and B ⊂ A and hence A = B.
Let A = {a, e, i, o, u} and B = {a, b, c, d}. Then, A is not a subset of B and B is not a subset of A.
Solved Example
Question: A = {1, 2, 3, 4} and B = {2, 3, 4, 5, 6, 7}. Is set A a subset of B?
Solution:
Given that A = {1, 2, 3, 4} and B = {2, 3, 4, 5, 6, 7}. We know that A is said to be the subset of B if every element of A is also in B. But, there is a number 1 in the set A which is not in B. So, A is not a subset of B.
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