If A = x ∈ R : | x - 2 | > 1 , B = x ∈ R : x 2 - 3 > 1 , C = x ∈ R : | x - 4 | ⩾ 2 and Z is the set of all integers, then the number of subsets of the set ( A ∩ B ∩ C ) c ∩ Z is _________.

Step-by-step solution

For First set A = x ∈ R : | x - 2 | > 1 ⇒ Value which A contains lies from x ∈ - ∞ , 1 ∪ 3 , ∞ For second set B = x ∈ R : x 2 - 3 > 1 ⇒ Value which B contains lies from x ∈ - ∞ , - 2 ∪ 2 , ∞ For third set C = x ∈ R : | x - 4 | ⩾ 2 ⇒ Value which C contains lies from x ∈ ( - ∞ , 2 ] ∪ [ 6 , ∞ ) Now, - ∞ , - 2 ∪ [ 6 , ∞ ) ∈ A ∩ B ∩ C Therefore, A ∩ B &#874