A logic network has two data inputs $$A$$ and $$B,$$ and two control inputs $${C_0}$$ and $${C_1}$$. It implements the function $$F$$ according to the following Table.

Implement the circuit using one $$4$$ to $$1$$ Multiplexor, one $$2$$-input Exclusive $$OR$$ gate, one $$2$$-input $$AND$$ gate, one $$2$$-input $$OR$$ gate and one Inverter.

What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in fig?

Let $$A = \left[ {\matrix{ {{a_{11}}} & {{a_{12}}} \cr {{a_{21}}} & {{a_{22}}} \cr } } \right]\,\,$$ and $$B = \left[ {\matrix{ {{b_{11}}} & {{b_{12}}} \cr {{b_{21}}} & {{b_{22}}} \cr } } \right]\,\,$$ be
two matrices such that $$AB=1.$$
Let $$C = A\left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]$$ and $$CD=1.$$
Express the elements of $$D$$ in terms of the elements of $$B.$$

Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is