Discrete Mathematics Answers

: Let p and q be the propositions.                                                        

p:  “I bought a lottery ticket.”

q:    “I won the million dollar jackpot on Friday.”  

Express each of these propositions as an English sentence.

a) ￢p                        b) ￢p →￢q

c)   p ↔q                     d) ￢p ∨(p ˄ q)

Write Inverse, Converse and Contrapositive, also apply implication law on the following statements:                                                                                                            

a)If it snows today. I will ski tomorrow.b)I come to class whenever there is going to be a quiz.c)I go to the beach whenever it is a sunny summer day.d) When I stay late, it is necessary that I sleep until noon.

Let A be the set of natural numbers multiples of 20 and B the set of natural numbers multiples of 15. Which is the set A ∩ B?

A.natural numbers multiples of 60

B. natural numbers multiples of 5

C. natural numbers multiples of 300

D. natural numbers multiples of 30

Let A be the set of natural numbers multiples of 20 and B the set of natural numbers multiples of 15. Which is the set A ∩ B?

A.natural numbers multiples of 60

B. natural numbers multiples of 5

C. natural numbers multiples of 300

D. natural numbers multiples of 30

Find the generating function of recurrence relation an+1_an=3n ,n less than 0 where ao=1

The bits string for A abd B are 1100101001 and 1011010110 respectively. Use bit string to find A intersection B compliment

Using laws of logic solve the following compound propositions. Also indicate the names

of laws.

[𝑝 ∧ (¬𝑝 ∨ 𝑞)] ∨ [𝑞 ∧ ¬(𝑝 ∧ 𝑞)]

Part 4 1. Consider the K-Maps given below. For each K- Map i. Write the appropriate standard form (SOP/POS) of Boolean expression. ii. Design the circuit using AND, NOT and OR gates. iii. Design the circuit only by using • NAND gates if the standard form obtained in part (i) is SOP. • NOR gates if the standard form obtained in pat (i) is POS.

. Check the validity of the following arguments (a) Hayder works hard. If Hayder works hard, then he is a dull boy. If Hayder is a dull boy, then he will not get the job. therefore, Randy will not get the job. (b) If it does not rain or if it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on. If the sailing race is held, then the trophy will be awarded. The trophy was not awarded. Thus, it rained.