Draw the logic circuit for the Boolean expression
We are given the Boolean expression: $$ ((x_1 \wedge ___ ___ ________ _______ ______ ____.
________ __________ ________ ____ ________ _________ _____ _________.
_______ ____ ____ ___ _______ ____ ____ ____ ______ _____ ________ ________.
____ _____ ______ ____ _________ ____ _______ ______ ___ ______.
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Find a recurrence relation for an , the number of ways to arrange cars in a row with n spaces if we can use Maruti 800, Tata Safari or Scorpio. A Tata Safari or Scorpio requires two spaces, whereas a Maruti 800 requires just one space. Assume that you have unlimited number of each type of car and we do not distinguish between 2 cars of the same type.
is Hamiltonian, how are m and n related? Justify your answer
Is there a 4-regular graph on 7 vertices? Justify your answer.
In the June, 2021 Term-End Examination of MTE-13, it was asked to give a direct and an indirect proof of the following statement.
such that a is even and a +b is even, then b is even."
One student gave an indirect proof as follows:
“Let b be m +1, which is an odd number. We already know a and a +b are even. If we substitute b + m +1 in a + b, it becomes a + m +1, which is an odd number. This contradicts the given statement. Hence b is an even number.”
What is wrong with the above proof ? Also give a correct direct and an indirect proof.
Define vertex connectivity and cut vertex set of any graph G. Find the vertex connectivity and cut vertex set for the following graph:
Show that if 7 colours are used to paint 50 bicycles and each bicycle is coloured with a single colour, at least 8 bicycles will have the same colour.
Find the Boolean expression in the DNF form for the function defined in tabular form below:
| x | y | z | |
| 1 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 |