Logic
State definitions and hypotheses precisely, construct a valid argument, and test it against a tempting counterexample.
Goal: recognise a logic problem from its wording, carry out the governing method, and check that the result is reasonable.
Practice deliberately
Work through Discrete Mathematics unit by unit, then test yourself under time.
Practice mode gives one hint and a worked explanation after every question. Test mode mixes all 7 units, holds the explanations until you submit, and then reports which units need another pass. The 8 questions printed further down this page are fixed, so you can read them and their worked answers without starting a set.
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Question 1Unit
Generated Discrete Mathematics question
Discrete Mathematics coverage and review map
Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.
This page follows the Discrete Mathematics syllabus unit by unit. For shorter mixed retrieval outside the course sequence, use discrete math practice questions with answers.
Proof methods
State definitions and hypotheses precisely, construct a valid argument, and test it against a tempting counterexample.
Goal: recognise a proof methods problem from its wording, carry out the governing method, and check that the result is reasonable.
Sets and relations
Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.
Goal: recognise a sets and relations problem from its wording, carry out the governing method, and check that the result is reasonable.
Counting
Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.
Goal: recognise a counting problem from its wording, carry out the governing method, and check that the result is reasonable.
Recurrence relations
Identify the generating pattern, distinguish term values from accumulated sums, and validate formulas with base cases and long-run behavior.
Goal: recognise a recurrence relations problem from its wording, carry out the governing method, and check that the result is reasonable.
Graph theory
Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.
Goal: recognise a graph theory problem from its wording, carry out the governing method, and check that the result is reasonable.
Number theory
Build number sense with exact representations, estimation, and inverse-operation checks before applying the skill in multi-step contexts.
Goal: recognise a number theory problem from its wording, carry out the governing method, and check that the result is reasonable.
Discrete Mathematics questions with worked answers
These 8 questions are printed in full on this page and are drawn across all 7 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.
Question 1: How many rows does a truth table need for a statement built from 5 different propositional variables?
- 32
- 25
- 10
- 64
Show the worked answer
- Each variable can be true or false, so each one doubles the number of rows.
- With n variables the table has 2^n rows.
- 2^5 = 2 x 2 x 2 x 2 x 2.
- That equals 32 rows.
Answer: 32
Question 2: What is the contrapositive of 'if n^2 is even, then n is even'?
- If n is odd, then n^2 is odd.
- If n is even, then n^2 is even.
- If n^2 is odd, then n is odd.
- If n is not even, then n^2 is even.
Show the worked answer
- The contrapositive of 'if P then Q' is 'if not Q then not P'.
- Here P is 'n^2 is even' and Q is 'n is even'.
- Not Q is 'n is odd' and not P is 'n^2 is odd'.
- So the contrapositive is 'if n is odd, then n^2 is odd', and it is logically equivalent to the original.
Answer: If n is odd, then n^2 is odd.
Question 3: Set A has 12 elements, set B has 18, and their union has 25. How many elements are in the intersection?
- 5
- 7
- 30
- 13
Show the worked answer
- Inclusion-exclusion says |A union B| = |A| + |B| - |A intersect B|.
- 12 + 18 = 30.
- So 25 = 30 - |A intersect B|.
- |A intersect B| = 30 - 25 = 5.
Answer: 5
Question 4: How many 4-letter strings can be made from the 26 letters if no letter repeats?
- 358,800
- 456,976
- 14,950
- 23,400
Show the worked answer
- The first position has 26 choices.
- Each later position loses one option: 25, then 24, then 23.
- Multiply: 26 x 25 = 650, and 24 x 23 = 552.
- 650 x 552 = 358,800.
Answer: 358,800
Question 5: A sequence has a(0) = 1 and a(n) = 2a(n - 1) + 3. What is a(4)?
- 61
- 29
- 45
- 31
Show the worked answer
- Apply the rule one step at a time.
- a(1) = 2(1) + 3 = 5 and a(2) = 2(5) + 3 = 13.
- a(3) = 2(13) + 3 = 29.
- a(4) = 2(29) + 3 = 61.
Answer: 61
Question 6: How many edges does the complete graph on 7 vertices have?
- 21
- 42
- 49
- 14
Show the worked answer
- In a complete graph every pair of vertices is joined exactly once.
- So the count is 7 choose 2.
- 7 choose 2 = (7 x 6) / 2.
- 42 / 2 = 21 edges.
Answer: 21
Question 7: What is 3^45 modulo 7?
- 6
- 1
- 3
- 2
Show the worked answer
- Fermat's little theorem gives 3^6 = 1 modulo 7, so powers repeat every 6 steps.
- 45 divided by 6 is 7 with a remainder of 3.
- So 3^45 has the same remainder as 3^3.
- 3^3 = 27, and 27 = 3(7) + 6, so the answer is 6.
Answer: 6
Question 8: A set has 9 elements. How many of its subsets contain one particular chosen element?
- 256
- 512
- 9
- 128
Show the worked answer
- Fix the chosen element as always included.
- Each of the other 8 elements is free to be in or out.
- That gives 2^8 possibilities.
- 2^8 = 256, which is exactly half of the 512 total subsets.
Answer: 256
Which unit each printed question belongs to
Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.
| Question | Unit | What it asks | Answer |
|---|---|---|---|
| 1 | Logic | How many rows does a truth table need for a statement built from 5 different propositional variables? | 32 |
| 2 | Proof methods | What is the contrapositive of 'if n^2 is even, then n is even'? | If n is odd, then n^2 is odd. |
| 3 | Sets and relations | Set A has 12 elements, set B has 18, and their union has 25. How many elements are in the intersection? | 5 |
| 4 | Counting | How many 4-letter strings can be made from the 26 letters if no letter repeats? | 358,800 |
| 5 | Recurrence relations | A sequence has a(0) = 1 and a(n) = 2a(n - 1) + 3. What is a(4)? | 61 |
| 6 | Graph theory | How many edges does the complete graph on 7 vertices have? | 21 |
| 7 | Number theory | What is 3^45 modulo 7? | 6 |
| 8 | Sets and relations | A set has 9 elements. How many of its subsets contain one particular chosen element? | 256 |
How the generated Discrete Mathematics sets are created
The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.
Questions about this Discrete Mathematics practice page
What does this page cover?
It covers all 7 Discrete Mathematics units listed above. Choose one unit for focused work, or mixed review to test method selection, and switch to test mode when you want all units mixed under time.
When can I see correct answers and explanations?
The 8 printed questions on this page keep their worked answers behind a toggle, so you can check any one of them straight away. In the generator above, practice mode explains each question as soon as you answer it, while test mode holds every explanation until you submit.
What should I do with a missed question?
Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.