Compre_DCS123

What is the logical translation of the following statement?"None of my friends are perfect."

Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?

• Everyone can fool some person at some time

• No one can fool everyone all the time

• Everyone cannot fool some person all the time

• No one can fool some person at some time

How many people must be in a room to guarantee that 3 of them were born in the same month?

• 25

• 36

• 37

• 93

By the pigeonhole principle, if 40 coins are distributed among 7 boxes, then there must be some box with at least ___ coins.

• 6

• 5

• 7

• 8

Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S is

• n and n

• n and 1

There are 30 people in a group. If all shake hands with one another , how many handshakes are possible?

• 870

• 435

• 30!

• 29! + 1

In a renowned software development company of 240 computer programmers 102 employees are proficient in Java, 86 in C#, 126 in Python, 41 in C# and Java, 37 in Java and Python, 23 in C# and Python, and just 10 programmers are proficient in all three languages. How many computer programmers are there those are not proficient in any of these three languages?

• 138

• 17

• 65

• 49

What is the logical translation of the following statement?"All birds can fly."

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 of the following about L, M, and N is Correct?

• Only L is TRUE

• Only M is TRUE

• Only N is TRUE

• L, M, and N are TRUE

Consider the following logical inferences.

I1: If it rains then the cricket match will not be played.

The cricket match was played.

Inference: There was no rain.

I2: If it rains then the cricket match will not be played.

It did not rain.

Inference: The cricket match was played.

Which of the following is TRUE?

• Both I1 and I2 are correct inferences

• I1 is correct but I2 is not a correct inference

• I1 is not correct but I2 is a correct inference

• Both I1 and I2 are not correct inferences