Question

Show the ralation R is set R of real numbers, defined as R = {(a, b) :a [tex] \leqslant [\tex] b^2} is neither reflexive nor symmetric not transitive. ​

Answer 1

Answer:

$\sf \large \:\underline{ \red{Answer} }:-$

R = {(a, b) : a < b^2

$It \: can \: be \: observed \: that [ \frac{1}{2}, \frac{1}{2} ] \: €R ,$

$\green{scine} \: \frac{1}{2 } > (\frac{1}{2} {)}^{2} = \frac{1}{4}$

$\boxed { \sf ∴ R \: is \: not \: reflexive }$

$now \: ,(1,4)€R \: as \: 1 \: < {4}^{2}$

$But ,4 \: is \: not \: symmetric$

∴ (4, 1) € R

$\boxed { \sf ∴ R \: is \: not \: symmetric. }$

\sf \large \:\underline{ \red{Now, } }:-[/tex]

$(3, 2) , (2, 1.5) € R$

$(as \: 3 \: < {2}^{2} = 4 \: and \: 2 \: < (1.5 {)}^{2} = 2.25)$

$But, 3 > (1.5 {)}^{2} = 2.25$

∴ (3, 1.5) € R

∴ R is not transitive

Answer 2

Answer:

here's your answer

Step-by-step explanation:

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