Test of Divisibility by 5 With Example

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ALOK_RAJ Asked Aug 14, 2023

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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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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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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 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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If $f: R \rightarrow R$ defined by $f(x)=\frac{3 x+5}{2}$ is an invertible function, find $f^{-1}$.

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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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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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In the set A={1,2,3,4,5} a relation R is defined by $R=\{(x, y) \mid x, y \in A$ and $x<y\}$. Then R is

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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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Test of Divisibility by 5 With Example

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