COMEDK · Maths · 20. Sets and Relations
The set \(\{-1,0,1\}\) is not a multiplicative group because of the failure of
- A Clostre law
- B Associative law
- C Identity law
- D Inverse law
Answer & Solution
Correct Answer
(D) Inverse law
Step-by-step Solution
Detailed explanation
We have, \[ A=\{-1,0,1\} \] Now, let \(e\) be the identity element. Then, \(\quad a \times e=a \Rightarrow e=1 \in A\) Again, \(a^{-1}\) be the inverse element. Then, \(\quad a \times a^{-1}=e\) \(\Rightarrow \quad a \times a^{-1}=1 \Rightarrow a^{-1}=\frac{1}{a}\) Now, for…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If for any \(2 \times 2\) square matrix \(A\),\(A(\operatorname{adj} A)=\left[\begin{array}{ll}8 & 0 \\ 0 & 8\end{array}\right]\), then find the value of \(\operatorname{det}(A)\).COMEDK 2022 Medium
- Samhita faces a three-headed dragon. She wins a 'Tactical medal' if she manages to defeat exactly one of the three heads.
The battle proceeds head-by-head under the following conditions:
The probability of defeating the first head is \(\dfrac{1}{3}\).
After a win: if she defeats a head, the probability of defeating the next head is \(\dfrac{2}{3}\).
After a loss: if she fails to defeat a head, the probability of defeating the next head is \(\dfrac{1}{4}\).
What is the probability that Samhita earns the 'Tactical medal'?COMEDK 2026 Medium - For a natural number \(n\), which one is the correct statement?COMEDK 2014 Medium
- The value of \(\lim _\limits{x \rightarrow \infty}\left(\dfrac{x^2-2 x+1}{x^2-4 x+2}\right)^{2 x}\) isCOMEDK 2023 Medium
- \(\text { The number of points of discontinuity of the rational function } f(x)=\dfrac{x^2-3 x+2}{4 x-x^3}\)COMEDK 2024 Medium
- The maximum value of \(\left(\frac{1}{x}\right)^{2 x^{2}}\) isCOMEDK 2018 Easy
More PYQs from COMEDK
- Density of \(3 \mathrm{M}\) solution of \(\mathrm{NaCl}\) is \(1.25 \mathrm{~g} / \mathrm{mL}\). The mass of the solvent in the solution isCOMEDK 2014 Medium
- Find the value of '\(b\)' such that the scalar product of the vector \(\hat{\imath}+\hat{\jmath}+\hat{k}\) with the unit vector parallel to the sum of the vectors \(2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}\) and \(b \hat{\imath}+2 \hat{\jmath}+3 \hat{k}\) is unityCOMEDK 2024 Medium
- \(\mathrm{H-}\)polaroid is prepared byCOMEDK 2013 Medium
- \(\int \dfrac{d x}{x \sqrt{4 x^2-9}}=\)COMEDK 2025 Medium
- In nucleic acids the nucleotides are linked byCOMEDK 2014 Easy
- The energy equivalent of \(1 \mathrm{~g}\) of a substance isCOMEDK 2014 Easy