Discrete math PROJECT 1-COUNTING PASSWORDs Choose 6 letters of the English alphabet including all the dfferent characters in your family name. (If you have more than 6 different char the first 6). Let Xbe the set of all lower case versions of the letters you have chosen. Also let N Respond to each of the following requirements 12.34.5) and M (3,45,6789) 0) Using correct notation, list the elements in the set X. Calculate X u x U NI and explain how the inclusion/exclusion rule works in this case. write an example of a password consisting of 6 characters with the flowing properties The first two characters are selected from set x. The remaining 4 characters are selected from the set N a) Let P be the set of all possible passwords constructed according to the rules given in part (0i) above How many passwords are there in P? That is, what is IPl v) Did you use the product rule or the sum rule to cakculate your answer to part a). Explain your reasoning v) Let Q be the set of all possible passwords constructed according to the rules given in part (il) above except that the remaining 4 characters are How many passwords are there in Q? v) Use the inclusion/exdlusion rule to calculate the number of passwords in PUQ.Explain your reasoning