$f_4$ = ((x, y) : ax + $by^2$ + c = 0, x, y $ \in $ R and a, b, c $ \in $ R. b $ \neq $ 0}Hence (D) ...

C is the correct answer.

$R_4$ = {(2, 4), (6, 12), (2, 6), (4, 8)}Hence (D) is the correct answer.

Domain of $R_2$ = {a, b, c, c} = {a, b, c}, Range of $R_2$ = {1, 2, 3, 4}

Domain of $ R_1$ = {a, a, b, b, c} = {a, b, c} , Range of $ R_1$ = {x, y, z}

Domain of R = {1, 3}; Range of R = {2, 1}.

Domain ={0, 2, 4, 6}, Range={10, 30, 60}

Domain ={1, 2, 3, 4}, Range={1, 2, 3, 4, 5}

Domain of R = the set of all first coordinates of members of R = {1, 2, 3, 4} Range of R = the set ...

R = {(x, y) / (x, y) $ \in $ A $ \times $ B, x < y} = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4...

S = {(x, y) / (x, y) $ \in $ A $ \times $ B, y / x}

$R = \{(x, y) / (x, y) \in A \times B, x = y^2 \}$

If ‘a’ is “perpendicular to” ‘b’ is denoted by a $ \perp $ b, then we have p $ \perp $ q, q $ \perp

If ‘a’ is “parallel to” ‘b’ is denoted by a || b, then we have p || n, n || p, m || q and q || m.

R = {(1, 4), (3, 2), (4, 1)}

i) $R_1$ = {(x, y) / x = y; x, y $ \in $ A},(ii) $R_2$ = {(x, y) / x < y; x, y $ \in $ A}, (ii...

$2^{36 }$

$R_3$ consists of all those ordered pairs of A $ \times $ B whose first coordinates are greater tha...

$R_2$ consists of all those ordered pairs of A $ \times $ B whose first coordinates are less than t...

$R_1$ consists of all those ordered pairs of A $ \times $ B whose first coordinates are equal to ...

(i) The relation ‘is less than’ in A $ \times $ A = {(5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8)}

(i) Anitha is the sister of Suneetha (ii) Mary is the wife of John (iii) Ravi is the brother of G...

Domain of R = Z, Range of R = Z

$2^6$

R = {(2, 8), (3, 27), (5, 125), (7, 343)}

Domain of R = {0, 1, 2, 3, 4, 5}, Range of R = {5, 6, 7, 8, 9, 10}

(i) R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6...

(i) R = {(x, y): y = x – 2; x $ \in $ P} or R = {(x, y): y = x – 2 for x = 5, 6, 7} (ii) R = {(5, 3

R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}

R = {(1, 6), (2, 7), (3, 8)}, Domain of R = {1, 2, 3}, Range of R = {6, 7, 8}

Domain of R = {1, 2, 3, 4}, Codomain of R = A = {1, 2, 3, …, 14}, Range of R = {3, 6, 9, 12}

We have, A $ \times $ B = {(1, 3), (1, 4), (2, 3), (2, 4)}. Since n (A $ \times $ B) = 4, the numbe...

Obvious that the relation R is “x is the square of y”.set-builder form, R = {(x, y): x is the square

(i) By the definition of the relation, R = {(1,2), (2,3), (3,4), (4,5), (5,6)}.The corresponding arr...

{-2, -1, 3, 4}Hence (B) is the correct answer.

2Hence (B) is the correct answer.

A = {-1, 1, 2}, B = {-2, 3}Hence (B) is the correct answer.

4Hence (B) is the correct answer.

(1, 1) $ \in $ A $ \times $ BHence (C) is the correct answer.

$ \{(a_1, x), (a_2, x), (a_3, x) (a_1, y), (a_2, y) (a_3, y) \}$Hence (B) is the correct answer.

the set of all points lying on the y-axis in two-dimensional spaceHence (C) is the correct answer.

{3, 5, 7}Hence (D) is the correct answer.

{(p, p, p), (p, p, q), (p, q, p), (p, q, q), (q, p, p), (q, p, q), (q, q, p), (q, q, q)}Hence (D) i...

$ 2^{35}$Hence (D) is the correct answer.

(2, 4), (2, 6), (2, 8), (3, 4), (3, 6), (3, 8), (4, 4), (4, 6), (4, 8)}

120

A $ \times $ (B $ \cap $ C) = (A $ \times $ B) $ \cap $ (A $ \times $ C)

A $\times $ (B $ \cup $ C) = (A $ \times $ B) $ \cup $ (A $ \times $ C)

A $ \times $ B = {1, 2, 3} $ \times $ {5, 6} = {(1, 5), (1, 6), (2, 5) (2, 6), (3, 5), (3, 6)}B $ \t...

(A $ \times $ B) $ \cap $ (A $ \times $ C) = {(1, 4), (2, 4), (3, 4)} $ \therefore $ A $ \times $ (B...