Algebra and Arithmetic

The SIGN function returns: 1 for positive numbers, 0 for zero, and -1 for negative numbers. Option D correctly states it returns 1 for positive values. Options A and C are wrong because positive values return 1, not >0 or 0.

The phrase “not negative” means any number that is zero or greater. The condition “>=0” includes zero and all positive numbers, satisfying the definition. In contrast, “=0” only covers zero, “>=1” omits zero, and “<=0” incorrectly includes negative values, so they are not correct.

For n-bit signed integers, the range is -2^(n-1) to 2^(n-1)-1. The negative side can go to -2^(n-1) (using the sign bit), while the positive side maxes at 2^(n-1)-1 since zero uses one positive value. This matches option B.

The postfix increment operator a++ adds 1 to a and returns the original value (before increment). It is equivalent to a = a + 1. The increment happens after the value is used in the expression.

Not negative means a value is greater than or equal to zero (>=0). This includes zero and all positive numbers. It doesn't mean equal to 0 only, or >=1 (which excludes zero), or <=0 (which would include negative numbers).

Not negative means the value is either zero or positive. In mathematical notation, this is x >= 0. A value greater than or equal to 1 would exclude zero, while less than or equal to 0 would only include negative numbers and zero.

A number that is 'not negative' cannot be less than 0. The number 0 itself is not negative, and all positive numbers are also not negative. Therefore, 'not negative' means the number is greater than or equal to 0 (x ≥ 0).

SQL and databases use multiple operators to express inequality: != is the most common, ^= is used in some SQL dialects (including Oracle), and <> is the SQL-92 standard operator. The !== operator is not a standard SQL comparison operator.

R = E[X²] - (E[X])² is the definition of variance, which is always non-negative because variance measures spread and cannot be negative. R = 0 only when the random variable is constant. R > 0 when the variable has any variation. Therefore R >= 0 is always true.

$$ \begin{array} AC + B\bar C &= AC_1 + B \bar C_1 \\ &= AC(B+\bar B) + B\bar C(A+\bar A) \\ &= ACB + AC\bar B + B\bar C A + B\overline{CA} \end{array} $$

We know that, If the four tense operators, P, F, H and G and following axions are $G (Q\rightarrow R)\rightarrow (GQ \rightarrow GR)$ $H (Q\rightarrow R) \rightarrow (HQ\rightarrow HR)$ $G - HQ \rightarrow Q$ $- H - GQ\rightarrow Q$

$(+AB)*C+(*DE)+(*FG)$ $= *+ABC+(*DE)+(*FG)$ $=+ + * + ABC * DE * FG$