Consider the following multiplexer where $$10, 11, 12, 13$$ are four data input lines selected by two address line combinations $${A_1}\,{A_0} = 00,01,10,11$$ respectively and $$f$$ is the output of the multiplex (or). $$EN$$ is the Enable input.

The function $$f(x,y,z)$$ implemented by the above circuit is

"If X then Y unless Z" is represented by which of the following formulas in propositional logic? (" $$\neg $$ " is negation, " $$ \wedge $$ " is conjunction, and " $$ \to $$ " is implication)

Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is

The binary relation $$S = \phi $$ (emply set) on set A = {1, 2, 3} is