Express the following statements in symbolic form.
i) There is a man in the park with blue eyes.
ii) Every blue-eyed man in the park is wearing a red hat.
iii) If a man wears no hat, then he has black eyes
i) Let the domain be all men in the park.
Let $B(x)$: $x$ has blue eyes.
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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.
write down and count all the partitions of the number 7. To verify your answer use the generating function for , Pn taking n= 7 in Theorem 5 (of Unit 5, Block2).
Draw three nonisomorphic induced subgraphs of the following graph, each having the same number of vertices. Justify your choice.
Express 5 x in terms of falling factorials and hence evaluate m S5 for m = 0,1,2,3,4,5.
Is the complement of the Peterson graph planar? Justify your answer.b) Is the complement of the Peterson graph planar? Justify your answer.
How many numbers from 0 to 759 are not divisible by either 3 or 7?
Solve the recurrence relation: