# GATE CSE 2014 SET-3

 Question 1
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?
 A Only L is TRUE. B Only M is TRUE. C Only N is TRUE. D L, M and N are TRUE.
Discrete Mathematics   Propositional Logic
Question 1 Explanation:
 Question 2
Let x and Y be finite sets and f:x$\rightarrow$Y be a function. Which one of the following statements is TRUE?
 A For any subsets A and B of x, |f(A$\cup$B)|=|f(A)|+|f(B)| B For any subsets A and B of x, f(A$\cap$B) =f(A)$\cap$f(B) C For any subsets A and B of x, |f(A$\cap$B)| = min{|f (A)| ,|f(B)|} D For any subsets S and T of Y, $f^{-1}(S\cap T)=f^{-1}(S)\cap f^{-1}(T)$
Discrete Mathematics   Set Theory
Question 2 Explanation:

 Question 3
Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L$\neq$G and that the size of L is at least 4. The size of L is _______.
 A 4 B 5 C 6 D 7
Discrete Mathematics   Group Theory
Question 3 Explanation:
 Question 4
Which one of the following statements is TRUE about every n x n matrix with only real eigenvalues?
 A If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. B If the trace of the matrix is positive, all its eigenvalues are positive. C If the determinant of the matrix is positive, all its eigenvalues are positive. D If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
Engineering Mathematics   Linear Algebra
Question 4 Explanation:
 Question 5
If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1$\cap$V2 is _______.
 A 1 B 2 C 3 D 4
Engineering Mathematics   Linear Algebra
Question 5 Explanation:

There are 5 questions to complete.