Discrete Mathematics
Q201.
In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking, the person replies the following "The result of the toss is head if and only if I am telling the truth." Which of the following options is correct?Q202.
What is the logical translation of the following statement? "None of my friends are perfect."Q203.
Consider the recurrence relation a_{1}=8, a_{n}=6n^{2}+2n+a_{n-1}. Let a_{99}= K \times 10^{4}. The value of K is .Q204.
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT?Q205.
Consider the following recurrence: \begin{aligned} f(1)&=1; \\ f(2n)&=2f(n)-1, & \text{for }n \geq 1; \\ f(2n+1)&=2f(n)+1, & \text{for }n \geq 1. \end{aligned}Then, which of the following statements is/are TRUE?MSQQ207.
Let p,q, r, s represent the following propositions. p: x\in{8,9,10,11,12} q: x is a composite number r: x is a perfect square s: x is a prime number The integer x\geq2 which satisfies \neg((p\Rightarrow q)\wedge (\neg r \vee \neg s)) is ________.Q208.
Given thatB(a) means "a is a bear"F(a) means "a is a fish" andE(a,b) means "a eats b"Then what is the best meaning of\forall x[F(x) \rightarrow \forall y(E(y, x) \rightarrow b(y))]Q209.
Which one of the following is NOT logically equivalent to \neg \exists x(\forall y(\alpha )\wedge \forall z(\beta ))?Q210.
Let H_1, H_2, H_3, ... be harmonic numbers. Then, for n \in Z^+, \sum_{j=1}^{n} H_j can be expressed as