Question

Is {h : h is a human being with 5 legs } = {x ∈ R : x

2 + 1 = 0}? Justify.
Hint: Find out elements in each set.​

Answer 1

SOLUTION :

GIVEN

Two sets are given by :

$1. \: \: \sf{} \{\: h : h \: is \: a \: human \: being \: with \: 5 \: legs \: \}$

$2. \: \: \sf{} \{ \: x \in \mathbb{R} \: : \: {x}^{2} + 1 = 0 \: \}$

TO CHECK

Are the sets are equal

CONCEPT TO BE IMPLEMENTED

EMPTY SET :

A set S is said to be an Empty set is S contains no element

$\sf{}It \: is \: denoted \: by \: \: \Phi$

EVALUATION

Let us denote the given two sets by A and B respectively

$\sf{}A = \{ \: h : h \: is \: a \: human \: being \: with \: 5 \: legs \: \}$

$\sf{}B = \{ \: x \in \mathbb{R} \: : \: {x}^{2} + 1 = 0 \: \}$

For the set A

Since all human being has five legs

So there is no element in the set A

$\therefore \: \: \sf{}A = \Phi$

Now for the set B

$\sf{} {x}^{2} + 1 = 0 \: \: gives \: \: x = i \: \: and \: \: - i$

Since i, - i are complex numbers

So there is no solution of the equation in the set of Real numbers

$\therefore \: \sf{}B = \Phi$

Since A and B are both Empty Sets

Hence A = B

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LEARN MORE FROM BRAINLY

If A, B and C are any three sets then prove

the following using venn-diagram

A∩(BUC) = (A∩B) U (A∩C)

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