Question 1 |

Let S be a set of consisting of 10 elements. The number of tuples of the form (A,B) such that A and B are subsets of S, and A\subseteq B is _______

49049 | |

59049 | |

3524 | |

854 |

Question 1 Explanation:

Question 2 |

If A=\{x, y, z\} and B=\{u, v, w, x\}, and the universe is \{s, t, u, v, w, x, y, z\}. Then (A \cup \bar{B}) \cap(A \cap B) is equal to

\{u,v,w,x\} | |

\{x\} | |

\{u,v,w,x,y,z\} | |

\{u,v,w\} |

Question 2 Explanation:

NOTE: This question is Excluded
for
evaluation. Originally all Options are wrong. We have modified one option.

Click here for detail solution by gateoverflow

Click here for detail solution by gateoverflow

Question 3 |

Consider the first order predicate formula:

\forall x[\forall z\; z|x\Rightarrow ((z=x)\vee (z=1))\Rightarrow \exists w(w> x)\wedge (\forall z \; z|w\Rightarrow ((w=z)\vee (z=1)))]

Here 'a|b' denotes that 'a divides b', where a and b are integers. Consider the following sets:

S1: {1, 2, 3, ..., 100}

S2: Set of all positive integers

S3: Set of all integers

Which of the above sets satisfy \varphi ?

\forall x[\forall z\; z|x\Rightarrow ((z=x)\vee (z=1))\Rightarrow \exists w(w> x)\wedge (\forall z \; z|w\Rightarrow ((w=z)\vee (z=1)))]

Here 'a|b' denotes that 'a divides b', where a and b are integers. Consider the following sets:

S1: {1, 2, 3, ..., 100}

S2: Set of all positive integers

S3: Set of all integers

Which of the above sets satisfy \varphi ?

S1 and S2 | |

S1 and S3 | |

S2 and S3 | |

S1,S2 and S3 |

Question 3 Explanation:

Question 4 |

Let U=\{1,2,,...n\}. Let A=\{(x,X)|x\in X,X\subseteq U\}. Consider the following two statements on |A|.

I. |A|=n2^{n-1}

II. |A|=\sum_{k=1}^{n}k\binom{n}{k}

Which of the above statements is/are TRUE?

I. |A|=n2^{n-1}

II. |A|=\sum_{k=1}^{n}k\binom{n}{k}

Which of the above statements is/are TRUE?

Only I | |

Only II | |

Both I and II | |

Neither I nor II |

Question 4 Explanation:

Question 5 |

The following paradigm can be used to find the solution of the problem in minimum time:

Given a set of non-negative integer and a value K, determine if there is a subset of the given set with sum equal to K:

Given a set of non-negative integer and a value K, determine if there is a subset of the given set with sum equal to K:

Divide and Conquer | |

Dynamic Programming | |

Greedy Algorithm | |

Branch and Bound |

Question 5 Explanation:

Question 6 |

Let N be the set of natural numbers. Consider the following sets.

P: Set of Rational numbers (positive and negative)

Q: Set of functions from {0, 1} to N

R: Set of functions from N to {0, 1}

S: Set of finite subsets of N.

Which of the sets above are countable?

P: Set of Rational numbers (positive and negative)

Q: Set of functions from {0, 1} to N

R: Set of functions from N to {0, 1}

S: Set of finite subsets of N.

Which of the sets above are countable?

Q and S only | |

P and S only | |

P and R only | |

P, Q and S only |

Question 6 Explanation:

Question 7 |

The symmetric difference of sets A={1,2,3,4,5,6,7,8} and B={1,3,5,6,7,8,9} is:

{1,3,5,6,7,8} | |

{2,4,9} | |

{2,4} | |

{1,2,3,4,5,6,7,8,9} |

Question 7 Explanation:

Question 8 |

Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements:

I. Each compound in U \ S reacts with an odd number of compounds.

II. At least one compound in U \ S reacts with an odd number of compounds.

III. Each compound in U n S reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

I. Each compound in U \ S reacts with an odd number of compounds.

II. At least one compound in U \ S reacts with an odd number of compounds.

III. Each compound in U n S reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

Only I | |

Only II | |

Only III | |

None |

Question 8 Explanation:

Question 9 |

A function f:\mathbb{N}^{+}\rightarrow \mathbb{N}^{+}, defined on the set of positive integers \mathbb{N}^{+}, satisfies the following properties:

f(n)=f(n/2) if n is even

f(n)=f(n+5) if n is odd

Let R={i|\exists j:f(j)=i} be the set of distinct values that f takes. The maximum possible size of R is ____.

f(n)=f(n/2) if n is even

f(n)=f(n+5) if n is odd

Let R={i|\exists j:f(j)=i} be the set of distinct values that f takes. The maximum possible size of R is ____.

1 | |

2 | |

3 | |

4 |

Question 9 Explanation:

Question 10 |

Suppose U is the power set of the set S={1,2,3,4,5,6}. For any T\inU, let |T| denote the number of elements in T and T' denote the complement of T. For any T,R\inU, let T\R be the set of all elements in T which are not in R. Which one of the following is true?

\forall X\in U \; (|X|=|X'|) | |

\exists X\in U \; \exists Y\in U \; (|X|=2,\; |Y|=3 \; and \; X \setminus Y=\phi ) | |

\forall X\in U \; \forall Y\in U \; (|X|=5,\; |Y|=5 \; and \; X \cap Y=\phi ) | |

\forall X \in U \; \forall Y\in U\; (X \setminus Y=Y' \setminus X') |

Question 10 Explanation:

There are 10 questions to complete.

There was an error in the question no 6, please update the option(d) to P, Q and S.

Thank You MOUNIKA DASA,

We have updated the option.

There is an error in question 40 in the last option it is ” S does not belong to Power set”

Thank You Aarti Mehra,

We have updated the option.