Chapter 2 : Relations and Functions
Q. If the set A has 3 elements and the set B={3, 4, 5} then find the number of elements in (A×B)?
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Q. If A×B={(a, x), (a, y), (b, x), (b, y)} Find A and B.
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Q. Let A={1, 2}, B={1, 2, 3, 4}, C={5, 6} and D={5, 6, 7, 8} Verify that
(i) A×(BC)=(A×B)(A×C)
(ii) A×C is a subset of B×D
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Q. If G={7, 8} and H={5, 4, 2}, find G×H and H×G.
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Q. Let A={1, 2} and B={3, 4}. Write A×B and find how many subsets will A×B have? List them.
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Q. Let A and B be two sets such that n(A)=3 and n(B)=2. If (x, 1), (y, 2), (z, 1) are in A×B find A and B where x, y and z are distinct elements
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Q. The cartesian product A×A has 9 elements among which are found (1, 0) and (0, 1). Find the set A and the remaining elements of A×A
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Q. If =A{1, 1} then find A×A×A.
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Q. State whether each of the following statements are true or false. If the statement is false rewrite the given statement correctly
(i) If P={m, n} and Q={n, m} then P×Q={(m, n), (n, m)}
(ii) If A and B are non-empty sets then A×B is a non-empty set of ordered pairs (x, y) such that xA and yB
(iii) If A={1, 2}, B={3, 4} then A×(Bϕ)=ϕ
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Q. If (x3+1, y23)=(53, 13) find the values of x and y
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Q. Let A={1, 2, 3, 4, 6} and R be the relation on A defined by {(a, b):a, bA , b is exactly divisible by a}
(i) Write R in roster form
(ii) Find the domain of R
(iii) Find the range of R
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Q. Define a relation R on the set N of natural numbers by R={(x, y):y=x+5, x is a natural number less than 4;x, yN}. Depict this relationship using roster form. Write down the domain and the range.
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Q. The figure shows a relationship between the sets P and Q. Write this relation in
(i) in set-builder form (ii) roster form

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Q. Let A={1, 2, 3, ...., 14}. Define a relation R from A to A by R={(x, y):3xy=0 where x, yA}. Write down its domain, co-domain and range.
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Q. Let R be the relation on Z defined by R= {(a, b):a, bZ, ab is an integer}. Find the domain and range of R.
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Q. Determine the domain and range of the relation R defined by R={(x, x+5):x{0, 1, 2, 3, 4, 5}}
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Q.

Write the relation R={(x, x3):x is a prime number less than 10}in roster form.

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Q. Let A={x, y, z} and B={1, 2}. Find the number of relations from A to B.
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Q. A={1, 2, 3, 5} and B={4, 6, 9}. Define a relation R from A to B by R={(x, y): the difference between x and y is odd xA, yB}. Write R in roster form
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Q. Which of the following relations are functions? Give reasons.
If it is a function determine its domain and range
(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
(iii) {(1, 3), (1, 5), (2, 5)}
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