Discrete Mathematics Answers

Let p and q be propositions. p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives.

1. You do not drive over 65 miles per hour.
2. You will get a speeding ticket if you drive over 65 miles per hour.
3. If you do not drive over 65 miles per hour, then you will not get a speeding ticket. 

Show, by the use of the truth table/matrix, that the statement  (p v q) ∧ [( ¬p) ∧ (¬q)] is a tautology.

Annulment Law on Boolean Algebra. Type it in MS WORD. Include examples and source of your research. Min. of 5 pages

a. Find the recursive definition for the sequence

i. 2 , 4 , 16 , 256 , ......

ii. 1 , 5 , 52 , 53 , 54 , ...

a.      Let A and B be sets as follows, A= {1,2,3,5,7} and B = {1,5,6,8}. Find:

i.            A∩B

ii.          | A∩B|

iii.        P(A∩B)

iv.        P(A) and P(B)

v.          | P(A) | and | P(B) |

vi.        The Cartesian product of A and B. vii.         |A|, |B| and hence find |A x B|  

In a high school 155 students are surveyed and ask which of the foreign languages they learn.45 learn spanish ,56 learn french,61 learn Chinese.22 learn spanish and french,17 learn spanish and Chinese while 24 learn french and Chinese.9 students don't learn any foreign language. What is the number taking all three subjects

Question 1

Let p: I get the job

q: I work hard

r: I get promoted

(a) Write the following proposition in terms of p, q, r and logical connectives.

“If I get the job and work hard, then I will get promoted.” (2 marks)

(b) Use your answer in part (i), state the converse, contrapositive and negation of the proposition in terms of p, q, r and logical connectives. Simplify your answers to the form without logical connectives “→”. (6 marks)

let Q( x,y) denote the statement 'x=y+5' , what is the truth value of Q(3,4)

Proof the following by using logical equivalences identities. Are these system specifications consistent by using Reasoning Method? a) ¬(p ∧ (p → ¬q))→¬p

b) ¬(q →¬p)→¬q

3. In how many ways can an elf climb a staircase of 15 stairs if each step it takes can cover 1 or 2 or 3 stairs? Explain why your solution is valid. (Hint: Work on fewer number of stairs first and try to generalize.)