4 MC question about propositional logic and logic circuits

Decide whether each of the following statements is true or false. The logical expression PQ can be implemented as a logic circuit containing exactly one NOT gate and one AND gate An expression which is equivaent to the logical expression P(QP) can be implemented as a logic circuit containing exactly one NOT gate and one OR gate For any logic circuit there is an equivalent circuit which uses only NOR gates For any logic circuit there is an equivalent circuit which uses only AND and OR gates Use logical equivalences to rewrite the following expressions so that they use only NAND operators, then using as few NAND gates as possible draw an equivalent logic circuit that uses only NAND gates. In each case give the number of gates in your circuit. PQ(PQ)(PR) For each of the following logical expressions find the Karnaugh map and its cover and then give the number of loops in the cover. xyz+xyz+xyz+xyz+xyz(x+y+z)+xyz(x+x+z)yzxyz+xyz(xyz)+yz Marked out of 7.00 Flag question For each logical expression find the Karnaugh map and its cover and then select, from the list (a)-(j) below, the minimal DNF that it is equivalent to. (a) z (f) (xyz) (b) xz+xz+yz+yz (g) xyz+xy+xz (c) y (h) x+y+z (d) xy+x (i) xy+xz+yz (e) xyz (j) xyz+xyz(xyz)(x+x+y+y)zxyz+xyzxyz+xyz+xyz+xyz((x+y+z)+xyz)(xyz)+x+y(xyz)+xyz