QuestionJune 5, 2025

5 thematics Let R be a relation from set A to set B. Which of the following is NOT true about the relation R^-1 a Range ofR^-1=Domain ofR b. RangeofR^-1subseteq A C. Domain ofR^-1=Range ofR d. Domain ofR^-1=B

5 thematics Let R be a relation from set A to set B. Which of the following is NOT true about the relation R^-1 a Range ofR^-1=Domain ofR b. RangeofR^-1subseteq A C. Domain ofR^-1=Range ofR d. Domain ofR^-1=B
5
thematics
Let R be a relation from set A to set B. Which of the following is NOT true about the relation
R^-1
a Range ofR^-1=Domain ofR
b. RangeofR^-1subseteq A
C. Domain ofR^-1=Range ofR
d. Domain ofR^-1=B

Solution
4.4(200 votes)

Answer

Statements b and d are NOT true about the relation R^{-1}. Explanation 1. Analyze the properties of inverse relation R^{-1} The inverse relation R^{-1} swaps the domain and range of R. Therefore, the domain of R^{-1} is the range of R, and the range of R^{-1} is the domain of R. 2. Evaluate each statement a. True: Range of R^{-1} is indeed the domain of R. b. False: Range of R^{-1} should be equal to set A, not just a subset. c. True: Domain of R^{-1} is the range of R. d. False: Domain of R^{-1} should be the range of R, not set B.

Explanation

1. Analyze the properties of inverse relation $R^{-1}$<br /> The inverse relation $R^{-1}$ swaps the domain and range of $R$. Therefore, the domain of $R^{-1}$ is the range of $R$, and the range of $R^{-1}$ is the domain of $R$.<br /><br />2. Evaluate each statement<br /> a. True: Range of $R^{-1}$ is indeed the domain of $R$.<br /> b. False: Range of $R^{-1}$ should be equal to set $A$, not just a subset.<br /> c. True: Domain of $R^{-1}$ is the range of $R$.<br /> d. False: Domain of $R^{-1}$ should be the range of $R$, not set $B$.
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