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={2,4,6}) and (B={1,2,3,4}), how many pairs ((x,y)) in (A\times B) satisfy (x-y) is positive?

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Answer and explanation

Cartesian product of sets

Practice questions

01 If (A={2,4,6}) and (B={1,2,3,4}), how many pairs ((x,y)) in (A\times B) satisfy (x-y) is positive?

02 If \(A=\{0,1,2,3\}\) and \(B=\{0,1,4,9\}\), how many ordered pairs \((x,y)\) in \(A\times B\) satisfy \(y=x^2\)?

03 If (A={1,2,3}), (B={1,2,3}), and (R={(x,y)\in A\times B:x+y\text{ is even}}), what is (n(R))?

04 If (A={1,2,3,4}), (B={1,2,3,4}), and (S={(x,y)\in A\times B:x+y=5}), what is (S)?

05 If (A={a,b,c}) and (B={1,2}), which pair belongs to (B\times A)?

06 If (A={1,2,3,4,5}) and (B={1,4,9,16,25}), how many pairs ((x,y)) in (A\times B) satisfy (y=x^2) and (x) is odd?

07 If (A={1,2,3}), (B={2,3,4}), and (T={(x,y)\in A\times B:x+y\text{ is prime}}), what is (n(T))?

08 If (A={1,2,3,4}) and (B={2,4,6,8}), how many pairs ((x,y)) in (A\times B) have (y) as a multiple of (x)?

09 If (A={2,3,5}) and (B={4,6,10,15}), how many pairs ((x,y)) in (A\times B) satisfy (\gcd(x,y)>1)?

10 If (A={1,2,3,4}) and (B={1,2,3,4}), how many pairs ((x,y)) in (A\times B) have (x+y) divisible by (3)?

11 If (A={1,2,3,4,5}) and (B={1,2,3,4,5}), how many pairs ((x,y)) in (A\times B) satisfy (x+y=xy)?

12 If (A={1,2,3,4}), (B={2,4,6}), (C={3,4,5}) and (D={4,6,8}), how many elements are in ((A\times B)\setminus(C\times D))?

13 If (A\times B={(1,2),(1,3),(4,2),(4,3)}), what are (A) and (B)?

14 If (A={a,b,c}), (B={1,2}), and (C={p,q,r,s}), what is (n((A\times B)\times C))?

15 If (A) has (m) elements and (B) has (n) elements and (n(A\times B)=n(B\times A)), choose the correct statement.

16 Under which condition is (A\times B=B\times A) definitely true?

17 If (A={1,2}) and (B={2,3}), what is (A\times B\cap B\times A)?

18 If (A={x:x\in\mathbb{N},x\le 5}) and (B={y:y\in\mathbb{N},y\text{ is prime},y<10}), how many pairs in (A\times B) have (a+b) even?

19 If (A={1,2,3,4}) and (B={2,4,6}), how many pairs in (A\times B) satisfy (a\mid b)?

20 If (A={0,1,2}) and (B={-1,0,1}), how many pairs in (A\times B) satisfy (ab=0)?

21 If (A={1,2,3}) and (B={1,2,3,4}), how many pairs in (A\times B) satisfy (a<b)?

22 If (A={2,3,5}) and (B={4,6,9,10}), how many pairs in (A\times B) satisfy (\gcd(a,b)=1)?

23 If (A={1,2,3,4}) and (B={3,4,5}), how many pairs are in ((A\times B)\setminus(B\times A))?

24 If (A={x\in\mathbb{Z}:-2\le x\le2}) and (B={y\in\mathbb{Z}:y^2=4}), how many pairs in (A\times B) satisfy (x+y=0)?

25 If (A={1,2}), (B={3,4}), and (C={5}), then (A\times(B\cup C)) equals which expression?

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