Tag: maths

If $A,B$ are two non-empty sets which of the following statement is false

If $A=\left{1, 2, 3\right}$, then the numbers of subsets of set $A$ containing element $3$, is 

Let ${ a } _{ 1 },{ a } _{ 2 },{ a } _{ 3 },............{ a } _{ 10 }$ be in G.P. with ${ a } _{ i }>0$ for $i=1,2,....,10$ and $S$ be the set of pairs $(r,k),r\quad k\in N$ ( the set of natural numbers) for which
$\left| { log } _{ e }{ a } _{ 1 }^{ r }{ a } _{ 2 }^{ k }\quad { log } _{ e }{ a } _{ 2 }^{ r }{ a } _{ 3 }^{ k }\quad { log } _{ e }{ a } _{ 3 }^{ r }{ a } _{ 4 }^{ k }\ { log } _{ e }{ a } _{ 4 }^{ r }{ a } _{ 5 }^{ k }\quad { log } _{ e }{ a } _{ 5 }^{ r }{ a } _{ 6 }^{ k }\quad { log } _{ e }{ a } _{ 6 }^{ r }{ a } _{ 7 }^{ k }\ { log } _{ e }{ a } _{ 7 }^{ r }a _{ 8 }^{ k }\quad { log } _{ e }{ a } _{ 8 }^{ r }{ a } _{ 9 }^{ k }\quad { log } _{ e }{ a } _{ 9 }^{ r }{ a } _{ 10 }^{ k } \right| =0$
Then the number of elements in S, is :

Classify $A = {x | x$ is a multiple of $3}$ as 'finite' or 'infinite'.

Classify $D = {x | x = 2^n, n \in N}$ as 'finite' or 'infinite'.

Classify $B = {y | y$ is a factor of $13}$ as 'finite' or 'infinite'.

The set of fractions between the natural numbers 3 and 4 is a :

If $A$ is finite set. Let $n(A)$ denote the number of elements in $A$ and $B$ are finite sets, $A\neq B$ and $n(A) = n(B)$. Then $n(A\cap B)$ is

Identify the type of Set
$A= { x| x \epsilon N, 2 \leq x \leq 3}$

A finite set $S$ is given by $S={x:x\in N: x\le15}.$ Find the cardinality of its power set.