GATE CSE 1997 | Question: 5.5

Question

Consider a logic circuit shown in figure below. The functions $f_1, f_2 \text{ and } f$ (in canonical sum of products form in decimal notation) are :

$f_1 (w, x, y, z) = \sum 8, 9, 10$

$f_2 (w, x, y, z) = \sum 7, 8, 12, 13, 14, 15$

$f (w, x, y, z) = \sum 8, 9$

 

The function $f_3$ is

• A. $\sum 9, 10$

• B. $\sum 9$

• C. $\sum 1, 8, 9$

• D. $\sum 8, 10, 15$

Comments

Great explanations

Answer 1

$f = (f_1 \wedge f_2) \vee f_3$

Since $f_1$ and $f_2$ are in canonical sum of products form, $f_1 \wedge  f_2$ will only contain their common terms- that is $f_1 \wedge f_2 = \Sigma 8$

Now, $\Sigma 8 \vee f_3 = \Sigma 8,9$
So, $f_3 = \Sigma 9$

Correct Answer: $B$

Comments

Its or gate. Why shouldn't we take the UNION? that is both 8 and 9 in the answer.

We just took out the coomon term?

---

AND gate behaves like Intersection, OR gate behaves like Union, EX-OR gate behaves set difference in set theory.

Reference:

• http://www.toves.org/books/logic/ 

---

Adding more to @Lakshman Patel RJIT Sir's comment:-

In set theory, the set difference between two sets is defined as the set of elements that are in the first set but not in the second set.

So in a way, we can say that an EX-OR gate behaves like a set difference operator, in the sense that it compares its inputs and produces a "true" output if the inputs are different, and a "false" output if the inputs are the same. However, it's important to note that an EX-OR gate is a logical operation and is not directly related to set theory in the way that set difference is.