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A binary relation R on N x N is defined as follows:
(a, b) R (c, d) if a <= c or b <= d.
Consider the following propositions:
P: R is reflexive
Q: R is transitive
 
Q. 
Which one of the following statements is TRUE?
  • a)
    Both P and Q are true.
  • b)
    P is true and Q is false.
  • c)
    P is false and Q is true.
  • d)
    Both P and Q are false.
Correct answer is option 'B'. Can you explain this answer?
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A binary relation R on N x N is defined as follows:(a, b) R (c, d) if ...
THEORY: REFLEXTIVE RELATION:   A relation ‘R’ on a set ‘A’ is said to be reflexive if, (xRx) for every x£A. Ex. If A= {1,2} And R, and P be a relation on AxA, defined as, R= {(2,2),(1,1)} => R is reflexive as it contains all pair of type (xRx). P= {(1,1)} => P is not reflexive relation on A, as it doesn’t contain (2,2).   TRANSITIVE RELATION: A relation ‘R’ on set ‘A’ is said to be transitive if (xRy) and (yRz), then (xRz) for every x,y,z £A. Ex: if A= {1,2} Let R be a relation on AxA, defined as, R= {(1,1),(1,2),(2,1)} => R is transitive.  SOLUTION: Given, (a, b) R (c, d) if a <= c or b <= d i.Check for reflexivity: if an element of set be (a,b) then, (a,b)R(a,b) should hold true. Here, a<=a or b<=b. So, (a,b)R(a,b) holds true. Hence, ‘R’ is reflexive. ii. Check for transitivity:  if elements of set be (2,3),(3,1) and(1,1) Then, (2,3)R(3,1) as 2<=3 And (3,1)R(1,1) as 1<=1 But (2,3)R(1,1) doesn’t hold true as 2>=1 and 3>=1. Hence, R is reflexive but not transitive. 
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A binary relation R on N x N is defined as follows:(a, b) R (c, d) if a <= c or b <= d.Consider the following propositions:P: R is reflexiveQ: R is transitiveQ.Which one of the following statements is TRUE?a)Both P and Q are true.b)P is true and Q is false.c)P is false and Q is true.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer?
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A binary relation R on N x N is defined as follows:(a, b) R (c, d) if a <= c or b <= d.Consider the following propositions:P: R is reflexiveQ: R is transitiveQ.Which one of the following statements is TRUE?a)Both P and Q are true.b)P is true and Q is false.c)P is false and Q is true.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A binary relation R on N x N is defined as follows:(a, b) R (c, d) if a <= c or b <= d.Consider the following propositions:P: R is reflexiveQ: R is transitiveQ.Which one of the following statements is TRUE?a)Both P and Q are true.b)P is true and Q is false.c)P is false and Q is true.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A binary relation R on N x N is defined as follows:(a, b) R (c, d) if a <= c or b <= d.Consider the following propositions:P: R is reflexiveQ: R is transitiveQ.Which one of the following statements is TRUE?a)Both P and Q are true.b)P is true and Q is false.c)P is false and Q is true.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer?.
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