If a set is defined by the constraints 'x is a real number and x^2 < 16', whi

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Question: If a set is defined by the constraints \'x is a real number and x^2 < 16\', which of the following is NOT an element of this set?

Options:

Correct Answer: 4

Solution:

4 is not an element of the set because it does not satisfy the constraint x^2 < 16 (since 4^2 = 16).

If a set is defined by the constraints 'x is a real number and x^2 < 16', which of the following is NOT an element of this set?

If a set is defined by the constraints 'x is a real number and x^2 < 16', which of the following is NOT an element of this set?

Step 1: Understand the constraint given in the question, which is 'x is a real number and x^2 < 16'.
Step 2: Rewrite the constraint to find the values of x that satisfy it. We need to find when x^2 is less than 16.
Step 3: Solve the inequality x^2 < 16. To do this, we can take the square root of both sides. This gives us -4 < x < 4.
Step 4: This means that x can be any real number between -4 and 4, but not including -4 and 4 themselves.
Step 5: Now, check the number 4. Calculate 4^2, which equals 16.
Step 6: Since 16 is not less than 16, the number 4 does not satisfy the constraint x^2 < 16.
Step 7: Therefore, 4 is NOT an element of the set defined by the constraint.

Inequalities – Understanding and solving inequalities involving real numbers.
Set Notation – Identifying elements that belong or do not belong to a defined set based on given constraints.