TMUA Counterexamples and Negations
TMUA often gives a statement and then asks which of a series of options is a counterexample to that statement (remember for 'If P then Q', statement S must satisfy P and not Q to be a counterexample). TMUA also occasionally gives a complex sentence involving 'For all', some', 'there exists' etc and asks for its negation. For those comfortable with converting 'word' sentences to Boolean logic, this is certainly one way to proceed, though not the only way.
For those so interested, we offer both one to one TMUA coaching on Counterexamples and Negations, as well as online group coaching via Zoom - 'TMUA Counterexamples, Negations and Other Logic' is Session #20 of 20. Check our TMUA Group Coaching Schedule page for dates when this session is available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on counterexamples and negations - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
[Note: Boolean Logic is not directly tested on TMUA, though it is useful in answering these types of questions]
- Teaser #431 - tests basic understanding of what constitutes a 'counterexample to 'If X then Y' - Fairly Mild
- Teaser #4 - tests how to negate a Boolean logic statement - Standard
- Teaser #470 - tests sufficiency of various inequality and modulus statements, often using counterexamples to disprove - Medium
- Teaser #475 - tests ability to negate a word statement on subsets - Medium
- Teaser #455 - tests how to negate a fairly complex Boolean logic statement - Medium
- Teaser #451 - tests which circle provides a counterexample to a statement - Medium
- Teaser #448 - tests when the fact that 143=11x13 can be used as a counterexample to statements - Medium
- Teaser #219 - tests negation of a Boolean logic expression - Medium
- Teaser #433 - tests negation of a Boolean logic expression - Medium
- Teaser #428 - tests whether '21=3x7' is a counterexample to a list of statements about primes - Medium
- Teaser #471 - tests which function provides a counterexample to an integral statement - Medium
[Note: We also have a 'Logic and Reasoning' playlist on our YouTube channel however the videos in this playlist are not all relevant to TMUA (some are too easy, some are too hard, and many cover topics not tested in TMUA).]
TMUA Past Questions on Counterexamples and Negations: SP p2 q4; SP p2 q9; SP p2 q17; 2016 p2 q5; 2016 p2 q18; 2017 p2 q5; 2017 p2 q16; 2017 p2 q17; 2018 p2 q3; 2018 p2 q6; 2018 p2 q12; 2019 p2 q4; 2019 p2 q7; 2020 p2 q4; 2020 p2 q8; 2021 p2 q4; 2021 p2 q10; 2022 p2 q3; 2022 p2 q10; 2023 p2 q3
Practice makes perfect - good luck in your studies!