If * be a binary operation on set of integers I defined by $a{ }^* b=3 a+4 b-2$, find the value of 4 * 5 .

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LEELADHAR YADAV Asked Aug 22, 2023

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LEELADHAR YADAV Asked Aug 22, 2023

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Let * be a binary operation on set of integers $I$, defined by $a{ }^* b=2 a+b-3$. Find the value of $3 * 4$

LEELADHAR YADAV Asked Aug 22, 2023

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If the binary operation * on the set of integers Z, is defined by a*b = a + 3b^2, then find the value 2 * 4 .

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Let * be a binary operation on Q defined by $a{ }^* b=\frac{3 a b}{5}$, Show that * is commutative as well as associative. Also find its identity element, if it exists.

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Consider the binary operation * on the set $\{1,2,3,4,5\}$ defined by $a^* b=\min \{a, b\}$. Write the operation table of the operation *.

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LEELADHAR YADAV Asked Aug 22, 2023

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If the binary operation * on the set Z of integers is defined by $a * b=a+b-5$, then write the identity element for the operation * in Z.

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by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 17, 2023

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Let A={1,2,3,4,5,6} and * be an operation A defined by $a{ }^* b=r$, where r is the least non-negative remainder when the product a b is divided by k. Operation * is binary operation if k=

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Let * be a binary operation on $Z$. If $a^* b=\left(a^2+b^3\right)^2$ where $a, b \in Z$ then the value of $5^* 3$ is

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Let * be a binary operation on Z × Z defined by $(a, b)^*(c, d)=(a+c, b+d) ;(a, b),(c, d) \in Z \times Z$. Find $(1,2) *(3,5)$ and $(4,3) *(1,0)$.

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Is * defined on the set {1,2,3,4,5} by a*b = l.c.m. of a and b binary operation?

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Let * be a binary operation on the set R defined by $a{ }^* b=a+b+a b, a, b \in R$. Solve the equation $2^*\left(3^{\star} x\right)=7$

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If $\oplus$ is a binary operation on R defined by $a \oplus b=\frac{a}{4}+\frac{b}{7}$ for $a, b \in R$, then show that : $(2 \oplus 5) \oplus 7 \neq 2 \oplus(5 \oplus 7)$.

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Let * be a binary operation on Z defined by $x^* y=x^2+y^2+x y ; x, y \in Z$. The value of $\left[\left(1^* 2\right)+\left(0^* 3\right)\right]^2$ is

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Let " be a binary operation on set Q of rational numbers defined as $a$ * $b=\frac{a b}{5}$. Write the identity for ", if any

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Let * be the binary operation on N given by a*b = LCM of a and b. Find the value of 20 * 16 . Is * (i) commutative (ii) associative?

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LEELADHAR YADAV Asked Aug 17, 2023

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Let * be a binary operation on Z. If a*b=2 ab where $a, b \in Z$ then the value of 19 * 16 is

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Chandan Asked Sep 12, 2023

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Is the binary operation * defined on set N, given by $a * b=\frac{a+b}{2}$ for all $a, b \in Q$, commutative?

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LEELADHAR YADAV Asked Aug 22, 2023

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Let $Z$ be the set of all integers and R be the relation on Z defined as $R=\{(a, b): a, b \in Z$, and $(a-b)$ is divisible by 5} Prove that $R$ is an equivalence relation.

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LEELADHAR YADAV Asked Aug 17, 2023

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Let * be a binary operation on Z defined by a∗b=a+b−15 for $a, b \in Z$. The identity element in Z, is

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LEELADHAR YADAV Asked Aug 17, 2023

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Let * be a binary operation on $\mathrm{N}$ defined by $\mathrm{a}^* \mathrm{~b}=2^{5 \mathrm{ab}} ; \mathrm{a}, \mathrm{b} \in \mathrm{N}$. then the binary operation * is

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Given a binary operation $: A \times A \rightarrow A$ with the identity element $e$ in $A$, an element $a \in A$ is said to be invertible with respect to the operation * if there exists an element $b$ in A such that $a^* b=e=b^* a$ and $b$ is called the inverse of $a$ and is denoted by ${a}^{-1}$.

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Let * be a binary operation on Z defined by a * b=a+b−15 . The inverse of element 21 in Z, ) is

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Consider the binary operation * on Q defined by $a$ * $b=a+12 b+a b$ for $a, b \in Q$. Show that * is not commutative.

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Let * be a binary operation on N given by a∗ b=HCF(a,b),a,b∈N . Write the value of 22∗4 .

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Show that ${ }^{\star}: R \times R \rightarrow R$ given by $(a, b) \rightarrow a+4 b^2$ is a binary operation.

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Let A=N × N and '*' be a binary operation onA defined by $(a, b)^*(c, d)=(a d+b c, b d)$. Show that A has no identity element.

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If * be a binary operation on set of integers I defined by $a{ }^* b=3 a+4 b-2$, find the value of 4 * 5 .

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