Test: Subsets & Supersets (April 12) - JEE MCQ

Null set is the subset of every set so Y ⊂ X and Y ⊂ Z.
Since set X is equal to set Z so, Z ⊂ X and X ⊂ Z.

Set of rational numbers { x: x=p/q where p and q are integers and q≠0}.
Set of real numbers is not a subset of X. Set of natural numbers, whole numbers, integers are subset of X.

• The set containing all objects or elements and of which all other sets are subsets is a Universal set.
• Here, option A has all the elements of set P, Q and R. So {1, 2, 3, 4, 5, 6, 7, 9} may be considered as universal set for all the three sets P, Q and R.

• We have, A^c in X = The set of elements in X which are not in A = 0,1
• {0} ∈ A^c w.r.t. X is false, because {0} is not an element of A^c in X.
• ϕ ∈ A^c in X is false because ϕ is not an element of A^c in X.
• {0} ⊂ A^c in X is correct because the only element of {0} namely 0 also belong to A^c in X.
• 0 ⊂ A^c in X is false because 0 is not a set.

• A set A is a proper subset of a set B if A is a subset of B and there is at least one element of B that's not an element of A.
• Thus, the void set is a subset of all sets, and it's a proper subset of every set except itself.

L.C.M of 4 and 6 is 12.

Given, A = {x:x is a multiple of 4}
              = {4,8,12,16,20,…}

and     B = {x:x is a multiple of 6}
              = {6,12,18,24,…}

∴A ∩ B = {12,24,…}
             = {x:x is amultiple of 12}

Number of elements in power set = 2⁷ = 128

• Number of proper subsets of a given set = 2^m - 1, where m is the number of elements.
• Here the number of elements is 3. So the number of proper subsets of A = 2³ - 1 = 7.

|x| < 1 ⇒ -1 < x < 1
∴ No natural number exists between (-1, 1).

Square brackets [a, b] implies that values of a and b should be included in the range of x i.e., a ≤ x ≤ b.