Mathematics

Cartesian product of sets

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In Class 11 Mathematics, under Relations and Functions, students learn how to form the Cartesian product of two sets as the set of all possible ordered pairs (a, b), where a belongs to the first set and b to the second. The topic explains why the order of elements matters, how to represent products using roster form and diagrams, and how to find their number of elements. This foundation helps students describe relations as subsets of a Cartesian product and understand domain and codomain.

Practice questions

01 If A = {1, 2}, B = {3}, and C = {4, 5, 6}, what is n(A × B × C)?

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Answer and explanation

Cartesian product of sets

Practice questions

01 If A = {1, 2}, B = {3}, and C = {4, 5, 6}, what is n(A × B × C)?

02 If A = {0, 1} and B = {0, 2}, which pair will not be in A × B?

03 If (A\subset B), which statement is correct for (C\times A) and (C\times B)?

04 If (A={1}) and (B={2}), what is the difference between (A\times B) and (B\times A)?

05 If (A={2,4,6}) and (B={1,5}), how many points are obtained when (A\times B) is shown as points?

06 If shirt color set (A={\text{red},\text{blue}}) and size set (B={\text{small},\text{medium},\text{large}}) are given, how many choices are in (A\times B)?

07 If (A={2,3,4}) and (B={6}), how many elements are in (B\times A)?

08 If (A={1,2,3}) and (B={4,5}), which pairs in (A\times B) have (3) as the first component?

09 If (A={5,7}) and (B={1,2,3}), which pairs of (A\times B) have second component (2)?

10 If (A={0,1}) and (B={2,3}), what is the correct number and form of elements of (A\times B)?

11 If A = {1, 2} and B = {3, 4, 5}, why is (2, 4) correctly placed in A × B?

12 If (A={x:x\in \mathbb{N},\ x\leq 2}) and (B={10,20}), how many elements are in (A\times B)?

13 If (A={1,2,3}) and (B={1,2,3}), how many pairs in (A\times B) have equal components?

14 If (A={-2,0}) and (B={1}), which is (A\times B)?

15 If (A={\text{Mon},\text{Tue}}) and (B={\text{morning},\text{evening}}), of which set is ((\text{Mon},\text{evening})) an element?

16 If (A={1,2}) and (B={3,4}), in which pairs will (4) appear as the second component in (A\times B)?

17 If (A={3,4}) and (B={5}), which statement is correct?

18 If (A={1,2}) and (B={3,4,5}), how many pairs in (A\times B) have the smallest element of (A) as the first component?

19 If (A={2,4,6}) and (B={1,2}), how many pairs in (A\times B) have the largest element of (B) as the second component?

20 If (A={1,2}) and (B={2,3}), how many pairs in (A\times B) have sum of both components equal to (4)?

21 If (A={1,3}) and (B={2,4}), how many pairs in (A\times B) have an odd sum of components?

22 If (A={2,4}) and (B={1,3}), how many pairs in (A\times B) have an even product of components?

23 If (A={1,2}) and (B={1,2,3}), how many pairs in (A\times B) have first component equal to second component?

24 If (A={0,1,2}) and (B={2,3}), how many ordered pairs in (A\times B) have the difference of both components equal to (1)?

25 If (A={1,4}) and (B={2,5}), which is the correct form of (A\times B)?

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