Question 1 |

Let X be a set and 2^X denote the powerset of X.

Define a binary operation \Delta on 2^X as follows:

A \Delta B=(A-B) \cup (B-A)

Let H=(2^X,\Delta ) . Which of the following statements about H is/are correct?

Define a binary operation \Delta on 2^X as follows:

A \Delta B=(A-B) \cup (B-A)

Let H=(2^X,\Delta ) . Which of the following statements about H is/are correct?

H is a group. | |

Every element in H has an inverse, but H is NOT a group. | |

For every A \in 2^X, the inverse of A is the complement of A. | |

For every A \in 2^X, the inverse of A is A. |

Question 1 Explanation:

Question 2 |

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 2 Explanation:

Question 3 |

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 3 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 4 |

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 4 Explanation:

Question 5 |

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 5 Explanation:

There are 5 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.

In Q7, options B and C are incorrect..

In Q11, options B and C are incorrect..

In Q11, options B and C are incorrect..