High School

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MCQ:

If we want to write a truth table representing the following equations:

\[ F1(x, y, z) = x + x'y + z' \]

\[ F2(x, y, z) = x'z + y \]

We will need:

A. 2 rows and 2 columns
B. 3 rows and 5 columns
C. 3 rows and 3 columns
D. 3 rows and 6 columns

Answer :

To represent the given equations in a truth table, we need 3 rows and 4 columns.

To write a truth table that represents the given equations, we need to consider the number of variables involved. In this case, there are three variables: x, y, and z. Each variable can have two possible values, 0 or 1. Therefore, for each variable, we need two rows in the truth table. As there are three variables, we need a total of 2^3 = 8 rows. For the output columns, F1(x,y,z) has a single output, so we need one output column. F2(x,y,z) also has a single output, so we need another output column. Therefore, we need 3 rows and 2 + 2 = 4 columns in total.

So the correct answer is not listed among the options provided. We need 3 rows and 4 columns for the truth table representation of the given equations.

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