Practice Lecture -14 (14.1.1) - Lecture -14 - Discrete Mathematics

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
State the arithmetic mean of the numbers 4 and 16.
Show hintHide hint
Add the numbers and divide by 2.
Question 2.
Write the binary representation of 12.
Show hintHide hint
What powers of 2 do sum to 12?
3Question 3.
What is the arithmetic mean of 6 and 14?
- 7
- 10
- 11
Show hintHide hint
Calculate the average.
4Question 4.
True or False: Every positive integer can be expressed as a sum of distinct powers of two.
- True
- False
Show hintHide hint
Think about how binary numbers work.
Question 5.
Prove by induction that for n = 2^k, the arithmetic mean is always greater than or equal to the geometric mean.
Show hintHide hint
Refocus on properly utilizing A and G through each inductive verification.
Question 6.
Given that 8 guests know each other, can you prove that there is no celebrity?
Show hintHide hint
Break down the definitions clearly to find contradictions.

5 more questions in this section. Enroll free to practise them all.