Answer :

given: A = {−1, 1}

To find: A × A × A

So, A × A = {(−1, −1), (−1, 1), (1, −1), (1, 1)}

And, A × A × A = {(−1, −1, −1), (−1, −1, 1), (−1, 1, −1), (−1, 1, 1), (1, −1, −1), (1, −1, 1), (1, 1, −1), (1, 1, 1)}

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State True or False for the following statements

If (x – 2, y + 5) = are two equal ordered pairs, then x = 4, .

Mathematics - ExemplarIf [x]^{2} – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, then

A. x ∈ [3, 4]

B. x ∈ (2, 3]

C. x ∈ [2, 3]

D. x ∈ [2, 4)

Mathematics - ExemplarState True or False for the following statements

The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y ∈ **Z**}

Let A = {3, 4, 5, 6} and R = {(a, b) : a, b ϵ A and a <b

(i) Write R in roster form.

(ii) Find: dom (R) and range (R)

(iii) Write R^{–1} in roster form

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Let R = {(a, b) : a, b, ϵ N and a < b}.

Show that R is a binary relation on N, which is neither reflexive nor symmetric. Show that R is transitive.

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Let A = (1, 2, 3} and B = {4}

How many relations can be defined from A to B.

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Is the given relation a function? Give reasons for your answer.

t = {(x, 3) | x is a real number.

Mathematics - ExemplarLet R = {(x, y): x, y ϵ Z and x^{2} + y^{2} ≤ 4}.

(i) Write R in roster form.

(ii) Find dom (R) and range (R).

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Let f : R^{+} → R : f(x) = log_{e} x. Find {x : f(x) = –2}.