Question

Check whether A{x: x² = 25 and 6x = 15) is an empty set or not? Justify your answer.
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Answer 1

Answer:

The set is empty as the equations have no common solutions.

Step-by-step explanation:

The set A is defined as,

$A=\{x:x^2=25 \ and \ 6x=15\}$

So A contains numbers that satisfy both the equations.

The solutions of the first equations are,

$x^2=25\implies x=5,-5$

The solution of the second equation is,

$6x=15\implies x=\dfrac{15}{6}$

We can see that there are no common solutions for these equations. Hence the set is empty.