If $$G$$ is a forest with $$n$$ vertices and $$k$$ connected components, how many edges does $$G$$ have?

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 of the following about L, M, and N is Correct?

A system uses $$3$$ page frames for storing process pages in main memory. It uses the Least Recently Used $$(LRU)$$ page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below? $$$4,7,6,1,7,6,1,2,7,2$$$

Consider a paging hardware with a TLB. Assume that the entire page table and all the pages are in the physical memory. It takes 10 milliseconds to search the TLB and 80 milliseconds to access the physical memory. If the TLB hit ratio is 0.6, the effective memory access time (in milliseconds) is______________.