Question

1. For some integer x, x is divisible by 5.
a. existential
b. universal
c. conditional
2. The square of a real number is nonnegative
a. existential
b. universal
c. conditional

Answer 1

1. The given statement is a 'Conditional' statement.

2. Given statement is a 'Universal' statement.

Step-by-step explanation:

1. Explanation

• Existential: Any existing integer 'x' is divisible by 5 but it may not be perfectly divisible due to which the reminder will be in decimals.

• Universal: It is not universal because, all the integers are not perfectly divisible by 5.

• Conditional: This is the correct option. Because, the integers with '0' or '5' in units place are only perfectly divisible by 5, which is a condition.

Hence, the given statement "any integer x is divisible by 5" is a conditional statement.

2. Explanation

• Existential: It is not the correct option because the given statement is a universal fact and law.

• Universal: This option is correct. The given statement "the square of a real number is non-negative" is a universal statement / law.

Let us take any real number 'x'. Whatever the number may be, it's square will be $x^{2}$ and not -$x^{2}$. Hence, it is universal mathematical law.

• Conditional: It is not a conditional statement, as the statement implies for all the existing real numbers without any condition.

Hence, the given statement "the square of a real number is non-negative" is a universal statement / law.