Test of Divisibility by 2 With Example

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ALOK_RAJ Asked Aug 14, 2023

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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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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 $g: R \rightarrow(0, \pi / 3]$ is defined by $g(x)=\cos ^{-1}\left(\frac{x^2-k}{1+x^2}\right)$. Then find the possible values of ' $k$ ' for which $g$ is surjective.

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

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Test of Divisibility by 2 With Example

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