The letter E is a vowel and therefore not included in the set of consonants.

The letter A is an element of the set as it is a vowel in the English alphabet.

The letter Z is not a vowel and therefore is not an element of the set defined by vowels.

The vowels in the English alphabet are A, E, I, O, and U. The letter Y is sometimes considered a vowel but is not classified as one in this context.

The correct representation of the set is {1, 2, 3, 4, 5, 6, 7, 8, 9}, as it includes all natural numbers less than 10.

The largest natural number less than 10 is 9, making it the largest element in the defined set.

The valid element of the set is 5, as it is a natural number and less than 10.

The element '5' is not part of the set because the constraint specifies that x must be less than 5.

The even natural numbers less than 20 are 2, 4, 6, 8, 10, 12, 14, 16, and 18. Therefore, 10 is included in the set.

The divisors of 12 are 1, 2, 3, 4, and 6, so 5 is not an element of this set.

The number '10' is not a multiple of 3, hence it is not an element of the set.

The set includes prime numbers less than 10, which are 2, 3, 5, and 7. The number 4 is not a prime number.

The number 4 is not a prime number, hence it is not included in the set of prime numbers less than 20.

The number 4 is not a prime number, hence it is not included in the set of prime numbers less than 20.

The number 21 is not included in the set as it does not meet the criteria of being less than 20.

All the operations listed can be validly performed on the set defined by the constraints.

1 is a natural number, while -1 and 0 are not considered natural numbers, and 2.5 is not an integer.

5 is a natural number and is less than 10, making it a valid element of the set defined by the given constraints.

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

The interval (-2, 2) represents all real numbers whose square is less than 4.

5 is not an element of the set because it does not satisfy the constraint 'x > 5'.

A is a vowel and meets the constraints of being a letter in the English alphabet.

9 is a multiple of 3 and less than 30, making it a valid element of the defined set.

Bob is the only student with a GPA above 3.5, thus he is included in the set.

Selling Price = 400 - (25% of 400) = 400 - 100 = $300. Profit = Selling Price - Cost Price = 300 - 250 = $50.

Let the marked price be x. Selling Price = x - 20% of x = 240. Thus, 0.8x = 240, so x = 300.

Let the marked price be x. Selling Price = x - (20% of x) = 0.80x. Thus, 0.80x = $80, so x = $80 / 0.80 = $100.

Selling Price = Cost Price - (Loss Percentage * Cost Price) = $200 - (0.10 * $200) = $200 - $20 = $180.

Selling Price = Cost Price - (Loss Percentage * Cost Price) = $500 - (0.10 * $500) = $500 - $50 = $450.

Let the cost price be x. Selling Price = Cost Price - (10% of Cost Price) = x - 0.10x = 0.90x. Thus, 0.90x = $90, so x = $90 / 0.90 = $100.