Mathematics
Write down all possible subsets of each of the sets given below :
(i) {1}
(ii) {3, 4}
(iii) {2, 3, 5}
(iv) Φ
(v) {c, d, e}
(vi) {a, b, c, d}
Answer
(i) {1}
Subsets are: Φ, {1}
(ii) {3, 4}
Subsets are: Φ, {3}, {4}, {3, 4}
(iii) {2, 3, 5}
Subsets are: Φ, {2}, {3}, {5}, {2, 3}, {3, 5}, {2, 5}, {2, 3, 5}
(iv) Φ
The empty set has only itself as a subset.
Subsets are: Φ
(v) {c, d, e}
Subsets are: Φ, {c}, {d}, {e}, {c, d}, {d, e}, {c, e}, {c, d, e}
(vi) {a, b, c, d}
Subsets are: Φ, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d}
Related Questions
State in each case, whether the given statement is true or false :
(i) If A is the set of all non-negative integers, then 0 ∈ A.
(ii) If B is the set of all consonants, then c ∈ B.
(iii) If C is the set of all prime numbers less than 80, then 57 ∈ C.
(iv) {x : x ∈ W, x + 5 = 5} is a singleton set.
(v) If D = {x : x ∈ W, x < 4}, then n(D) = 4.
(vi) {a, b, c, 1, 2, 3} is not a set.
(vii) {1, 2, 3, 1, 2, 3, 1, 2, 3,……………} is an infinite set.
(viii) 0 ∈ Φ.
(ix) {3, 5} ∈ (1, 3, 5, 7, 9).
Indicate whether the given statement is true or false :
(i) {Triangles} ⊆ {Quadrilaterals}
(ii) {Squares} ⊆ {Rectangles}
(iii) {Rhombuses} ⊆ {Parallelograms}
(iv) {Natural numbers} ⊆ {Whole numbers}
(v) {Integers} ⊆ {Whole numbers}
(vi) {Composite numbers} ⊆ {Odd numbers}
Write down all possible proper subsets of each of the sets given below :
(i) {x}
(ii) {p, q}
(iii) {m, n, p}
(iv) {1, 2, 3, 4}
Write down :
(i) The set C of letters of the word 'PAPAYA'.
(ii) All subsets of C.
(iii) All proper subsets of C.