Discrete Mathematics Answers

Prove that for all integers n, n(n + 2)(n + 4) is divisible by 3.

Prove that for all integers a, b, c such that c =/= 0, if ac|bc then a|b.

Prove that for all integers a, b, c if a|b then ac|bc

Find a counter-example to the following statement:

For all real numbers x > 1, 1/x^2+1 ≤ 1/2^x+1

Prove that the conditional proposition and its contrapositive are logically equivalent suing the truth table.

In how many ways can one select 7 member committee from 10 distinct persons if only three persons qualify to be chairperson?

According to information obtained from mathematics department regarding three mathematics units done by 100 students, those who are doing calculus are 45, those doing discrete are 49 and those doing statistics are 38. Those doing calculus and discrete are 17, those doing calculus and statistics are 12 and those doing the three units are 5. Use Venn diagram to find the number of students doing discrete and statistics but not calculus.

write the following boolean expressions in an equivalent sum of product canonical form in three variables x1, x2, and x3:
1. x1*x2 ?
3. (x1+X2)'*X3

How many 8-bits sequences that start with the same two bits or their fourth and fifth bits are equal or end with the same two bits are there?

If we reduce the number of elements by two, the number of permutations reduces thirty times. Find the number of elements.