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?
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?
Only L is TRUE. | |
Only M is TRUE. | |
Only N is TRUE. | |
L, M and N are TRUE. |
Question 1 Explanation:
Question 2 |
Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?
For any subsets A and B of x, |f(A\cupB)|=|f(A)|+|f(B)| | |
For any subsets A and B of x, f(A\capB) =f(A)\capf(B) | |
For any subsets A and B of x, |f(A\capB)| = min{|f (A)| ,|f(B)|} | |
For any subsets S and T of Y, f^{-1}(S\cap T)=f^{-1}(S)\cap f^{-1}(T) |
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\neqG and that the size of L is at least 4. The size of L is _______.
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7 |
Question 3 Explanation:
Question 4 |
Which one of the following statements is TRUE about every n x n matrix with only real
eigenvalues?
If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. | |
If the trace of the matrix is positive, all its eigenvalues are positive. | |
If the determinant of the matrix is positive, all its eigenvalues are positive. | |
If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive. |
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\capV2 is _______.
1 | |
2 | |
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4 |
Question 5 Explanation:
There are 5 questions to complete.