Question

Which equations are true for the values of XY and Z? (Select three options)

a) XY - Z = XY - Z
b) X - Y = Z - Y
c) XY + Z = XY + Z
d) X + Y = Z + Y
e) XY * Z = XY * Z

Answer 1

The equations that are always true regardless of values assigned to the variables X, Y, and Z are the mathematical identities: a) XY - Z = XY - Z, c) XY + Z = XY + Z, and e) XY * Z = XY * Z. Options b) and d) cannot be confirmed without specific values.

Step-by-step explanation:

To determine which equations are true for the values of variables X, Y, and Z, we should evaluate each option separately. However, even without specific values for X, Y, and Z, we can assess several of the given options as mathematical identities that are always true. Here's how we can approach each option:

• a) XY - Z = XY - Z is always true because it is an identity. Both sides of the equation are the same, basically stating that a value is equal to itself.
• c) XY + Z = XY + Z is also always true as it is the same identity as the one in option a, but with addition instead of subtraction.
• e) XY * Z = XY * Z again, is a trivial identity that is always correct.

Options b) and d) are not guaranteed to be true and may depend on the specific values of X, Y, and Z. Without additional context or values for these variables, we cannot affirm that they are true.