Discrete Mathematics Answers

Find, showing all working, a recursive denition of the sequence with general

term

tn = 3 (n + 1)!/2n ; n >= 1

What is the difference between an outcome and an event?

show that p↔q and (p∧q)∨(¬p∧¬q) are logically equivalent

Show that ¬(¬p) and p are logically equivalent.

Choose the best answer: ANTI SYMMETRIC, TRANSITIVE RELATION, SYMMETRIC RELATION, REFLEXIVE RELATION

1. {(3,5)(5,3) (2,4)(4,5)}

2. {(3,1)(1,3)}

3. {(3,1)(2,3)(5,6)(6,5)}

4. {(1,3)(5,3)(7,5)}

5. {(8,9)(9,7)(8,7)}

6. {(4,2)(2,4)}

7. {(1,5)(2,5)(3,5)}

8. {(5,5)(5,6)(6,5)(6,6)(6,7)(7,6) (7,7)}

9. {(6,5)(5,4)(6,4)}

10. {(7,6)(6,5)(7,5)}

11. {(3,1)(1,3)}

12. {(4,3)(3,5)(4,5)}

13. {(6,6)(6,5)(5,5)(5,4)(4,4)}

14. {(6,5)(7,6)(4,5)(5,4)}

15. {(3,3)(4,4)(4,5)(5,4)(5,5)}

A survey of 100 college students revealed the following information about their enrolment in Mathematics, Political Science, and Sociology courses. Twenty-six take Mathematics; 65 take Political Science; 65 take Sociology; 14 take Mathematics and Political Science; 13 take Mathematics and Sociology; 40 take Political Science and Sociology; 8 take Mathematics, Political Science and Sociology. How many students are taking both Mathematics and Sociology but not Political Science?

Draw the composite table for the operation * defined by x*y = x,

for every x , y ϵ S = {a, b, c, d}

Use a truth table to determine whether the given statement is a tautology or self-contradiction.

1. ~[p ∧ ( ~p v q)] v q

2. [p ∧ ( ~p v q)] v q

 (p ∧ r ∧ t) ↔ (q ∧ t) 

The set S consists of all integers from 1 to 2007 inclusive. For how many

elements n in S is f(n)=2n³+n²-n-2 over n²-2 an integer?