$A = {x : x \in R, x^{2} = 16 and 2 x = 6}$ Represent hte given set in roaster form. [3 Marks]

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Solution

Given $A = {x : x \in R, x^{2} = 16 and 2 x = 6}$ ...(0.5 marks)

$A$ is the set of common solutions of equations $x^{2} = 16 and 2 x = 6$ ...(0.5 marks)
As $x^{2} = 16 \Rightarrow x = \pm 4$ ...(0.5 marks)
ans $2 x = 6 \Rightarrow x = 3$ ...(0.5 marks)

There is no value of $x$ which satisfies both the given equations.
The set $A$ is an empty set or a null set. ...(0.5 marks)

Thus, $A = {}$ . ...(0.5 marks)

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