Consider the $$ALU$$ shown below

If the operands are in $$2's$$ complement representation, which of the following operations can be performed by suitably setting the control lines $$K$$ and $${C_0}$$ only ( + and - denote addition and subtraction respectively)?

The following resolution rule is used in logic programming. Derive clause $$\left( {P \vee Q} \right)$$ from clauses $$\left( {P \vee R} \right)$$, $$\left( {Q \vee \neg R} \right)$$.

Which of the following statements related to this rule is FALSE?

Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$, the values of $$P\,(A\,\left| {B) \,} \right.$$ and $$P\,(B\,\left| {A) \,} \right.$$ respectively are

Let $$A$$ be a sequence of $$8$$ distinct integers sorted in ascending order. How many distinct pairs of sequence, $$B$$ and $$C$$ are there such that
i) Each is sorted in ascending order.
ii) $$B$$ has $$5$$ and $$C$$ has $$3$$ elements, and
iii) The result of merging $$B$$ $$C$$ gives $$A$$?