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Relations And Functions
Write down all the subsets of the following sets
(i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) φ
(a) A = {a}
Number of elements in set A = 1
Number of subsets = 21 = 2
∴ The subsets are φ, {a}
(b) A = {a, b}
Number of elements in set A = 2
Number of subsets = 22 = 4
∴ The subsets are φ, {a}, {b}, {a, b}
(c) A = {1, 2, 3}
Number of elements in set A = 3
Number of subsets = 23 = 8
∴ The subsets are φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} and {1, 2, 3}
(d) φ = { }
Number of elements = 0
Number of subsets = 20 = 1
∴ The subsets is φ
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Fill in the blanks in the following table:
Numbers |
Closed under |
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Addition |
Subtraction |
Multiplication |
Division |
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Rational numbers |
Yes |
Yes |
No |
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Integers |
Yes |
No |
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Whole numbers |
... |
Yes |
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Natural numbers |
No |
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i9 + i19
3(7 + i7) + i(7 + i7)
Express each of the complex number given in the form of a + ib.
(1 - i) - (-1 + i6)
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