## Practice Test on Math Relation

Here in practice test on math relation will help the students to get more ideas about the questions on math relation. The questions are mainly related to **ordered pairs, Cartesian products of two sets, representation of math relation** and also **domain and range of a relation**. Depending on these topics there are various questions related to practice test on math relation worksheet.

**1.** Let A = {1, 3, 5, 7} and B = {p, q, r}. Let R be a relation from A into B defined by R = {(1, p), (3, r), (5, q), (7, p), (7, q)} find the domain and range of R.

**2.** Let A = {2, 4, 6} and B = {x, y, z}.

State which of the following are relation from A into B

(i) R_{1} = {(2, x), (y, 4), (6, z)}

(ii) R_{2} = {(4, y) (y, 4)}

(iii) R_{3} = {(2, x) (4, y) (6, z)}

**3.** Let A = {3, 4, 5, 6} B = {1, 2, 3, 4, 5, 6} Let R = {(a, b) : a ∈ A, b ∈ B and a < b}. Write R in the roster form. Find its domain and range.

**4.** Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Let R be A relation on A defined by R = {a, b} : a ∈ A, b ∈ A, a is a multiple of b}. Find R, domain of R, range of R.

**5.** Determine the range and domains of the relation R defined by R = {(x - 1), (x + 2) : x ∈ (2, 3, 4, 5)}

**6.** Let A = {1, 2, 3, 4, 5, 6} Define a relation R from A to A by R {(x, y) : y = x + 2}

• Depict this relation using an arrow diagram.

• Write down the domain and range of R

**7.** The adjoining figure shows a relation between the set A and B. Write this relation in

(i) Set builder form.

(ii) Roster form.

(iii) Find domain and range.

**8.** If A = {1, 4, 9, 16} and B = {1, 2, 3} Let R be a relation 'is square of’ from A to B. Find R domain and range of R.

**9.** Let A = {3, 4, 5} and B = {6, 8, 9, 10, 12}. Let R be the relation 'is a factor of' from A to B. Find R.

**10.** Adjoining figure shows relation between A and B. Write relation in

(i) Set builder form.

(ii) Roster form.

(iii) Find domain and range of R.

Answers for practice test on math relation will help the students to check the exact answers of the given questions.

### Answers:

**1.** Domain = {1, 3, 5, 7} Range = {p, r, q}

**2.** R

_{3} **3.** R ={(3, 4) (3, 5) (3, 6) (4, 5) (4, 6) (5, 6)}

Domain = {3, 4, 5} Range = {4, 5, 6}

**4.** R = {(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (7, 1) (8, 1) (9, 1) (10, 1) (4, 2) (6, 2) (8, 2) (10, 2) (6, 3) (9, 3) (8, 4) (10, 5)}

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

**5.** Domain = {1, 2, 3, 4} Range = {4, 5, 6, 7}

**6.** Domain = {1, 2, 3, 4} Range = {3, 4, 5, 6}

**7.** R = {(x, y) : y = 3x, x ∈ A, y ∈ B } R = {(1, 3) (2, 6) (3, 9) (4, 12) (5, 15)}

Domain = {1, 2, 3, 4, 5} Range = {3, 6, 9, 12, 15}

**8.** Domain = {1, 4, 9} Range = {1, 2, 3}

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

**9.** R = {(3, 6) (3, 9) (4, 8) (5, 10)}

**10.** R = {(x, y) : x = y^{2}, x ∈ A,y ∈ B} = {(1, 1) (1, -1) (4, 2) (4, -2) (9, 3) (9, -3) (16, 4) (16, -4)}

Domain = {1, 4, 9, 16} Range = {1, -1, 2, -2, 3, -3, 4, -4}

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