IGNOU MTE 12 2026 - . State which of the following statements are true and which are false

Question

. State which of the following statements are true and which are false. Give reasons for your answer with a short proof or a counter example.
a) The intersection of finite number of convex sets is not convex.
b) If value of the $2 \times 2$ matrix game $\begin{bmatrix} 1 & 2 \\ p & 4 \end{bmatrix}$ is 4, then $p \ge 4$ .
c) If 10 is added to each of the entries of the cost matrix of a $3 \times 3$ assignment problem, then the total cost of an optimal assignment for the changed cost matrix will increase by 10.
d) For maximization LP model, the simplex method is terminated when all values $c_j - z_j \ge 0$ .
e) The dummy source or destination in a transportation problem is added to prevent solution from becoming degenerate.

09 Jan 2026

Answer :

Word Count : 229

a) False. The intersection of a finite number of convex sets is always convex. Reason: Let (C_1, C_2, \dots, C_n) be convex sets. For any (x, y \in \bigcap_{i=1}^n C_i), since each (C_i) is convex, (\lambda x + (1-\lambda)y \in C_i) for all (\lambda \in [0,1]). Therefore, (\lambda x + (1-\lambda)y \in \bigcap_{i=1}^n C_i). b) False. Consider the matrix [

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