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1. Equal Set is defined as two sets having the same elements. Two sets A and B can be equal only on the condition that each element of set A is also the element of set B. Also, if two sets happen to be the subsets of each other, then they are stated to be equal sets.
2. Natural Numbers are the numbers which are positive integers and includes numbers from 1 till infinity (∞). These numbers are countable and are generally used for calculation purpose. The set of natural numbers is represented by the letter “ N ”.
3. In set theory, the power set of a Set A is defined as the set of all subsets of the Set A including the Set itself and the null or empty set. It is denoted by P(A). Basically, this set is the combination of all subsets including null set, of a given set.
4. Solve →
(i) x + y + z = 3(x - y + z)
⇒ x + y + z = 3x - 3y + 3z
⇒ 2x - 4y + 2z = 0
⇒ 2(x - 2y + z) = 0
⇒ x - 2y + z = 0
(ii) 3y + 2 = 2(x + z)
⇒ 3y + 2 = 2x + 2z
⇒ 2x - 3y + 2z - 2 = 0
(iii) 2x + 2z + y = 2(3z + y)
⇒ 2x + 2z + y = 6z + 2y
⇒ 2x - y - 4z = 0
6. (i) A - (B - A)
= {1, 4, 5, 6, 8, 9, 12}
(ii) A - (C - B)
= {2, 3, 5, 8, 12}
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