The number of group homomorphisms from

Let $X$ be a non-empty set and $P(X)$ be the set of all subsets of $X$. On $P(X)$, define two operations $\ast$ and $\Delta$ as follows: for $A,B\in P(X)$,

• $A\ast B=A\cap B$ (Intersection of sets)
• $A\Delta B=(A\cup B)\setminus (A\cap B)$ (Symmetric difference of sets)

Which of the following statements is true?

Let G be a group of order 2020 .

Which of the following statements are necessarily true?

Let G be a simple group of order 168. How many elements of order 7 

does it have?

How many generators of a cyclic group of order 36 have ?

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Which of the following equations can occur as the class equation of  group of order 10?

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Let G be any finite group. Which one of the following is necessarily true ?

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The number of group homomorphisms from

Let $X$ be a non-empty set and $P(X)$ be the set of all subsets of $X$. On $P(X)$, define two operations $\ast$ and $\Delta$ as follows: for $A,B\in P(X)$,

• $A\ast B=A\cap B$ (Intersection of sets)
• $A\Delta B=(A\cup B)\setminus (A\cap B)$ (Symmetric difference of sets)

Which of the following statements is true?

Let G be a group of order 2020 .

Which of the following statements are necessarily true?