In the Karnaugh map shown below, $$X$$ denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

A set of Boolean connectives is functionally complete if all Boolean function can be synthesized using those, Which of the following sets of connectives is NOT functionally complete?

A sample space has two events A and B such that probabilities $$P\,(A\, \cap \,B)\, = \,1/2,\,\,P(\overline A )\, = \,1/3,\,\,P(\overline B )\, = \,1/3$$.
What is P $$P\,(A\, \cup \,B)\,$$?

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that the studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?