Mathematics Questions and Answers – Cartesian Product of Sets

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This set of Mathematics Multiple Choice Questions & Answers focuses on “Cartesian Product of Sets”.

1. If P X Q is an empty set then which of the following is a null set?
a) only P
b) only Q
c) either P or Q
d) both P and Q
View Answer

Answer: c
Explanation: If either set P or set Q is a null set then P X Q is an empty set.
i.e. if P is Φ or Q is Φ then P X Q = Φ.
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2. If (a, b) = (x, y) then___________
a) a=x
b) a=y
c) a=y and b=x
d) a=x and b=y
View Answer

Answer: c
Explanation: Two ordered pairs are said to be equal if and only if their corresponding elements are equal i.e. a=x and b=y.

3. If set P has 4 elements and set Q has 5 elements then find the number of elements in P X Q.
a) 9
b) 45
c) 20
d) 54
View Answer

Answer: c
Explanation: If set P has m elements and set Q has n elements then P X Q has m*n elements.
Here, m=4 and n=5 therefore P X Q has 4*5=20 elements.
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4. If (x+2, y-3) = (5,7) then find values of x and y.
a) x=3 and y=10
b) x=3 and y=4
c) x=7 and y=4
d) x=7 and y=10
View Answer

Answer: a
Explanation: Two ordered pairs are said to be equal if and only if their corresponding elements are equal. x+2=5 => x=3
y-3=7 => y=10
Hence, x=3 and y=10.

5. Is (a, b) = (b, a)?
a) True
b) False
View Answer

Answer: b
Explanation: Since (a, b) is an ordered pair i.e. order of first and second element matters and hence they can’t be interchanged. So, (a, b) ≠ (b, a).
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6. If P X Q has 10 elements then which is not possible?
a) n(P)=1 and n(Q)=10
b) n(P)=10 and n(Q)=1
c) n(P)=2 and n(Q)=5
d) n(P)=5 and n(Q)=4
View Answer

Answer: d
Explanation: If set P has m elements and set Q has n elements then P X Q has m*n elements.
m*n=10 => if m=1 then n=10,
if m=2 then n=5,
if m=5 then n=2 and if m=10 then n=1.

7. If P = Q then P X Q = Q X P is true or not?
a) True
b) False
View Answer

Answer: a
Explanation: Let P = (x, y) and Q = (a, b)
P X Q = {(x, a), (x, b), (y, a), (y, b)}
Q X P = {(a, x), (a, y), (b, x), (b, y)}
If P = Q i.e. x=a and y=b then P X Q = {(a, a), (a, b), (b, a), (b, b)}
Q X P = {(a, a), (a, b), (b, a), (b, b)}.
Hence P X Q = Q X P.
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8. If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set A.
a) {1}
b) {1, 2}
c) {1, a}
d) {a, b, c}
View Answer

Answer: b
Explanation: In each ordered pair of A X B, first element belongs to set A and second element belongs to set B.
1,2 ∈ A so, A = {1, 2}.

9. If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set B.
a) {1}
b) {1, 2}
c) {1, a}
d) {a, b, c}
View Answer

Answer: d
Explanation: In each ordered pair of A X B, first element belongs to set A and second element belongs to set B.
a, b, c ∈ B so, B = {a, b, c}.
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10. If set A has 2 elements and set B has 3 elements then how many subsets does A X B have?
a) 6
b) 8
c) 32
d) 64
View Answer

Answer: d
Explanation: If set A has m elements and set B has n elements then A X B has m*n elements.
We know, a set has 2r subsets if it has r number of elements.
Here, A X B has 2*3 = 6 elements. So, number of subsets of A X B will be 26 i.e. 64.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter