Question 4. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) € R if and only if a) a is taller than b. b) a and b were born on the same day. c) a has the same first name as b. d) a and b have a common grandparent.

TLOP1P The Asker · Advanced Mathematics

Transcribed Image Text: 4. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) € R if and only if a) a is taller than b. b) a and b were born on the same day. c) a has the same first name as b. d) a and b have a common grandparent.
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Transcribed Image Text: 4. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) € R if and only if a) a is taller than b. b) a and b were born on the same day. c) a has the same first name as b. d) a and b have a common grandparent.
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8U7CUA

a) Q is not taller than Q. So R is not reflexive.  Q is taller than b does not imply b is taller than ​​​​​Q. So R is not symmetric. Hence R is not antisymmetric also. Let aRb and bRc.  Q is taller than b and b is taller than ( implies Q is taller than (. So R is transitive. b) a and a born on the same day. So R is reflexive. a and b born on the same day implies b and a born on the same day. So R is symmetric. Let aRb and bRa. But a may not be equal to b. So R is not antisymmet ... See the full answer