The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. That is the probability that it will rain today and tomorrow?

The number of equivalence relations on the set $$\left\{ {1,2,3,4} \right\}$$ is

The determination of the matrix $$$\left[ {\matrix{ 6 & { - 8} & 1 & 1 \cr 0 & 2 & 4 & 6 \cr 0 & 0 & 4 & 8 \cr 0 & 0 & 0 & { - 1} \cr } } \right]\,\,is$$$

Let $$A = ({a_{ij}})$$ be and n-rowed square matrix and $${I_{12}}$$ be the matrix obtained by interchanging the first and second rows of the n-rowed Identity matrix. Then$${AI_{12}}$$ is such that its first