Answer problem 3 a and b and describe how to do it as if it someone’s first time learning it 10:27 shyam.nitk.ac.in Show that the set (NOR) of operators is complete. (d) Find a formula equivalent to a (bACAd) using only the connectives (and not the constants TRUE and FALSE). Find the shortest such formula it have more or fewer symbols than the formula a (bACAd)? The NAND operator is often called the Sheffer stroke and is denoted at The NOR operator is often called the Pierce arrow and is denoted as p q. 3. The connective if-then-else is defined by the following truth table: if p then q clser T T T F T T F T F F T F F F F T T F FF This connective is key in binary decision diagrams (BDDs), which provide one dard way for manipulation of propositional formulas in computer programs. F ample, BDDs have been widely used by computer-chip designers in showing th circuits in the chips they design match the specifications for those chips. (In language, the connective is often called just ITE) (a) Find a formula equivalent to if a then if b then c else d else if e then d else c using only the connectives A, v. and Chapter Review (b) Find a formula equivalent to if a then if b then c else d else if e then d else c in CNF (c) Find a formula equivalent to-a using only the if-then-else connective ar stants T and F. (d) Find a formula equivalent to (a vbvc)A(a v-v d) A (-ev-d only the if-then-else connective and constants T and F 4. Find a DNF for the condition that there are an even number of l’s in the three strings p. q. and r. Draw a combinatorial network to represent the DNF. C simplify the combinatonal circut using the properties of a boolean algebra?