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Easy

Question

The relation ‘is subset of’ on the power set $P left parenthesis A right parenthesis$ of a set $A$ is

Symmetric
Anti-symmetric
Equivalence relation
None of these

The correct answer is: Anti-symmetric

The relation is not symmetric, because $A subset of B$ does not imply that $B subset of A.$ But, it is anti-symmetric because
$A subset of B$ and $B subset of A rightwards double arrow A equals B$

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Let $U$ be the universal set for sets $A$ and $B$ such that $n open parentheses A close parentheses equals 200 comma n open parentheses B close parentheses equals 300$ and $n open parentheses A intersection B close parentheses equals 100.$ Then, $n left parenthesis A ´ intersection B ´ right parenthesis$ is equal to 300, provided that $n left parenthesis blank U right parenthesis$ is equal to

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parallel

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parallel

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The void relation on a set $A$ is

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parallel

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parallel

Statement 1: $1 to the power of 99 end exponent plus 2 to the power of 99 end exponent plus horizontal ellipsis plus 100 to the power of 99 end exponent$ is divisible by 10100
Statement 2: $a to the power of n end exponent plus b to the power of n end exponent$ is divisible by $a plus b$ if $n$ is odd

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Statement 2: $a to the power of n end exponent plus b to the power of n end exponent$ is divisible by $a plus b$ if $n$ is odd

Statement 1:Let $F subscript 1 end subscript open parentheses n close parentheses equals 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction$ , then $not stretchy sum from r equals 1 to n of F subscript 1 end subscript open parentheses r close parentheses equals open parentheses n plus 1 close parentheses F subscript 1 end subscript open parentheses n close parentheses minus n.$
Statement 2: $fraction numerator 1 to the power of negative 1 end exponent plus 2 to the power of negative 1 end exponent plus 3 to the power of negative 1 end exponent plus... plus n to the power of negative 1 end exponent over denominator n end fraction greater than open parentheses fraction numerator 1 plus 2 plus 3 plus... plus n over denominator n end fraction close parentheses to the power of negative 1 end exponent$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus plus... fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator n to the power of 2 end exponent over denominator not stretchy sum n end fraction$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator 2 n over denominator left parenthesis n plus 1 right parenthesis end fraction$

Statement 1:Let $F subscript 1 end subscript open parentheses n close parentheses equals 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction$ , then $not stretchy sum from r equals 1 to n of F subscript 1 end subscript open parentheses r close parentheses equals open parentheses n plus 1 close parentheses F subscript 1 end subscript open parentheses n close parentheses minus n.$
Statement 2: $fraction numerator 1 to the power of negative 1 end exponent plus 2 to the power of negative 1 end exponent plus 3 to the power of negative 1 end exponent plus... plus n to the power of negative 1 end exponent over denominator n end fraction greater than open parentheses fraction numerator 1 plus 2 plus 3 plus... plus n over denominator n end fraction close parentheses to the power of negative 1 end exponent$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus plus... fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator n to the power of 2 end exponent over denominator not stretchy sum n end fraction$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator 2 n over denominator left parenthesis n plus 1 right parenthesis end fraction$

Statement 1:If an infinite G.P. has 2^nd term $x$ and its sum is 4, then $x$ belongs to $left parenthesis negative 8 comma blank 1 right parenthesis$
Statement 2:Sum of an infinite G.P. is finite if for its common ratio $r comma blank 0 less than open vertical bar r close vertical bar less than 1$

Statement 1:If an infinite G.P. has 2^nd term $x$ and its sum is 4, then $x$ belongs to $left parenthesis negative 8 comma blank 1 right parenthesis$
Statement 2:Sum of an infinite G.P. is finite if for its common ratio $r comma blank 0 less than open vertical bar r close vertical bar less than 1$

parallel

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