Mathematics
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}
Sets
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Answer
(i) {x}
Proper Subset is Φ
(ii) {p, q}
Proper Subsets are: Φ, {p}, {q}
(iii) {m, n, p}
Proper Subsets are: Φ, {m}, {n}, {p}, {m, n}, {n, p}, {m, p}
(iv) {1, 2, 3, 4}
Proper Subsets are: Φ, {1}, {2}, {3}, {4} {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4} {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}
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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}
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(i) {1}
(ii) {3, 4}
(iii) {2, 3, 5}
(iv) Φ
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(vi) {a, b, c, d}
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(iii) All proper subsets of C.
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