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If \( \Large R \subset A \times B\ and\ S \subset B \times C \) be two relations, then \( \Large \left(SOR\right)^{-1} \) is equal to:

A) \( \Large S^{-1}OR^{-1} \)
B) \( \Large R^{-1}OS^{-1} \)
C) SOR
D) ROS

Correct Answer:


B) \( \Large R^{-1}OS^{-1} \)

Description for Correct answer:

\( \Large R^{-1} \rightarrow B\ to\ A,\ S^{-1} \rightarrow C to B \)

\( \Large \therefore R^{-1}OS^{-1}\ is\ also\ from\ C\ to\ A\) \( \Large and\ \left(SOR^{-1}\right)\ is\ also\ from\ C\ to\ A \)
Hence \( \Large \left(SOR\right)^{-1} = R^{-1}OS^{1} \)

Part of solved Set theory questions and answers : >> Elementary Mathematics >> Set theory

Comments

Similar Questions

1). If \( \Large A = \{ x:x\ is\ multiple\ of\ 4 \} \) and \( \Large B = \{ x:x\ is\ multiples\ of 6 \} \) then \( \Large A \subset B \) consists of all multiples of:

A). 16

B). 12

C). 8

D). 4

2). The relation "less than" in the set of natural numbers is:

A). only symmetric

B). only transitive

C). only reflexive

D). equivalence relation

3). The solution set of \( \Large 8x \equiv 6 \left(mod\ 14\right),\ x \epsilon z \) are:

A). \( \Large \left[ 8 \right] \cup \left[ 6 \right] \)

B). \( \Large \left[ 8 \right] \cup \left[ 14 \right] \)

C). \( \Large \left[ 6 \right] \cup \left[ 13 \right] \)

D). \( \Large \left[ 8 \right] \cup \left[ 6 \right] \cup \left[ 13 \

4). Consider the following relations:
\( \Large 1.\ A-B=A- \left(A \cap B\right) \)
\( \Large 2.\ A= \left(A \cap B\right) \cup \left(A-B\right) \)
\( \Large 3.\ A- \left(B \cup C\right) = \left(A-B\right) \cup \left(A-C\right) \)
which of these is/are correct?

A). (1) and (3)

B). (2) only

C). (2) and (3)

D). (1) and (2)

5). Let \( \Large f: \left(-1,\ 1\right)\rightarrow B \), be a function defined by \( \Large f \left(x\right)=\tan -1\frac{2x}{1-x^{2}} \), then is both one-one and onto when B is the interval:

A). \( \Large \left(-\frac{ \pi }{2},\ \frac{ \pi }{2}\right) \)

B). \( \Large \left[ -\frac{ \pi }{2},\ \frac{ \pi }{2} \right] \)

C). \( \Large \left[ 0,\ \frac{ \pi }{2} \right] \)

D). \( \Large \left(0,\ \frac{ \pi }{2}\right) \)

6). The function of \( \Large f \left(x\right)= log \left(x+\sqrt{x^{2}+1}\right) \) is:

A). an even function

B). an odd function

C). a periodic function

D). neither an even nor an odd function

7). If \( \Large f:R \rightarrow R \) satisfies \( \Large f \left(x+y\right) = f \left(x\right) = f \left(x\right)+f \left(y\right) \) for all \( \Large x,\ y,\ \epsilon R\ and\ f \left(1\right)=7 \), then \( \Large \sum^{n}_{r=1}f \left(r\right) \) is:

A). \( \Large \frac{7n}{2} \)

B). \( \Large \frac{7 \left(n+1\right) }{2} \)

C). \( \Large 7n \left(n+1\right) \)

D). \( \Large \frac{7n \left(n+1\right) }{2} \)

8). A function of from the set of natural numbers to integers defined by \( \Large f \left(n\right) = \frac{\frac{n-1}{2},\ when\ n\ is\ odd}{-\frac{n}{2},\ when\ n\ is\ even} \) is:

A). one-one but not onto

B). onto but not one-one

C). one-one and onto both

D). neither one-one nor onto

9). The relation "is subset of on the power set P(A) of set A is:"

A). symmetric

B). antisymmetric

C). equivalence relation

D). none of these

10). In a college of 300 students, every student read 5 newspaper and every newspaper is read by 60 students. The number of newspaper is:

A). at least 30

B). at most 20

C). exactly 25

D). none of these