counterexample

Who acts: counterexample, that, general statement, primes, you, none · What happens: be, show, find, fly, win, end · To what, where: one example, 2 counterexample, claim, rectangle, counterexample, argument · Speech: someone speaks here

«counterexample» in the school dictionary: its meaning for a pupil and its 6 examples, every sentence parsed by Mova itself — its syntax tree, a dependency tree in the style of Universal Dependencies, and its pragmatics clause by clause. The word in the dictionary, with its sense in the lessons: counterexample in the school dictionary.

Meaning 1

Usage: maths, logic — kept apart, not parsed.

A counterexample is one example that shows a general statement is false.

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	A	a	DET	Definite=Ind PronType=Art	2 counterexample	det
2	counterexample	counterexample	NOUN	Number=Sing	5 example	nsubj
3	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	5 example	cop
4	one	one	NUM	NumForm=Word NumType=Card	5 example	nummod
5	example	example	NOUN	Number=Sing	root	root
6	that	that	PRON	PronType=Rel	7 shows	nsubj
7	shows	show	VERB	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	5 example	appos
8	a	a	DET	Definite=Ind PronType=Art	10 statement	det
9	general	general	ADJ	Degree=Pos	10 statement	amod
10	statement	statement	NOUN	Number=Sing	12 false	nsubj
11	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	12 false	cop
12	false	false	ADJ	Degree=Pos	7 shows	ccomp
13	.	.	PUNCT	_	5 example	punct

#	verb	tense, mood	who	what, whom	other	roles by
1	is a	present	a counterexample	one example		tree rules
2	show	present	that			vn transfer_mesg-37.1.1-1-1 «NP V»: agent=Agent
3	is	present	a general statement		false property	tree rules

One row per clause the reader finds. «not said here»: a role filled from the clause above. «roles by»: a VerbNet class and frame when one fits the verb, else the reader's rules on the tree.

Example 1

2 is a counterexample to the claim that all primes are odd.

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	2	2	NUM	NumForm=Digit NumType=Card	4 counterexample	nummod
2	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	4 counterexample	cop
3	a	a	DET	Definite=Ind PronType=Art	4 counterexample	det
4	counterexample	counterexample	NOUN	Number=Sing	root	root
5	to	to	ADP	_	7 claim	case
6	the	the	DET	Definite=Def PronType=Art	7 claim	det
7	claim	claim	NOUN	Number=Sing	4 counterexample	nmod
8	that	that	SCONJ	_	12 odd	mark
9	all	all	DET	PronType=Tot	10 primes	det
10	primes	prime	NOUN	Number=Plur	12 odd	nsubj
11	are	be	AUX	Mood=Ind Number=Plur Person=3 Tense=Pres VerbForm=Fin	12 odd	cop
12	odd	odd	ADJ	Degree=Pos	7 claim	acl
13	.	.	PUNCT	_	4 counterexample	punct

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	is a	present		a 2 counterexample				to the claim	tree rules
2	is	present	all primes	the claim not said here				odd property	tree rules

Example 2

Can you find a counterexample to Every square is a rectangle? (There is none.)

Sentence 1: Can you find a counterexample to Every square is a rectangle?

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	Can	can	AUX	VerbForm=Fin	3 find	aux
2	you	you	PRON	Case=Nom Person=2 PronType=Prs	3 find	nsubj
3	find	find	VERB	VerbForm=Inf	root	root
4	a	a	DET	Definite=Ind PronType=Art	5 counterexample	det
5	counterexample	counterexample	NOUN	Number=Sing	11 rectangle	nsubj
6	to	to	ADP	_	8 square	case
7	Every	every	DET	PronType=Tot	8 square	det
8	square	square	NOUN	Number=Sing	5 counterexample	nmod
9	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	11 rectangle	cop
10	a	a	DET	Definite=Ind PronType=Art	11 rectangle	det
11	rectangle	rectangle	NOUN	Number=Sing	3 find	ccomp
12	?	?	PUNCT	_	3 find	punct

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	find	can	you						vn declare-29.4-1-1 «NP V what S_INF»: agent=Agent
2	is a	present	a counterexample to every square	a rectangle					tree rules

Sentence 2: (There is none.)

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	(	(	PUNCT	_	3 is	punct
2	There	there	PRON	PronType=Dem	3 is	expl
3	is	be	VERB	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	root	root
4	none	none	PRON	PronType=Neg	3 is	nsubj
5	.	.	PUNCT	_	3 is	punct
6	)	)	PUNCT	_	3 is	punct

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	be	present	none			there			vn exist-47.1 «NP V»: agent=Theme

Example 3

One counterexample shows the rule is false.

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	One	one	NUM	NumForm=Word NumType=Card	2 counterexample	nummod
2	counterexample	counterexample	NOUN	Number=Sing	3 shows	nsubj
3	shows	show	VERB	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	root	root
4	the	the	DET	Definite=Def PronType=Art	5 rule	det
5	rule	rule	NOUN	Number=Sing	7 false	nsubj
6	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	7 false	cop
7	false	false	ADJ	Degree=Pos	3 shows	ccomp
8	.	.	PUNCT	_	3 shows	punct

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	show	present	One counterexample						vn transfer_mesg-37.1.1-1-1 «NP V»: agent=Agent
2	is	present	the rule					false property	tree rules

Example 4

A penguin is a counterexample to All birds can fly.

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	A	a	DET	Definite=Ind PronType=Art	2 penguin	det
2	penguin	penguin	NOUN	Number=Sing	5 counterexample	nsubj
3	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	5 counterexample	cop
4	a	a	DET	Definite=Ind PronType=Art	5 counterexample	det
5	counterexample	counterexample	NOUN	Number=Sing	root	root
6	to	to	SCONJ	_	10 fly	mark
7	All	all	DET	PronType=Tot	8 birds	det
8	birds	bird	NOUN	Number=Plur	10 fly	nsubj
9	can	can	AUX	VerbForm=Fin	10 fly	aux
10	fly	fly	VERB	VerbForm=Inf	5 counterexample	acl
11	.	.	PUNCT	_	5 counterexample	punct

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	is a	present	a penguin	a counterexample					tree rules
2	fly	can	all birds						vn spatial_configuration-47.6-1 «NP V»: agent=Theme

Example 5

She found a counterexample and won the argument.

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	She	she	PRON	Case=Nom Gender=Fem Number=Sing Person=3 PronType=Prs	2 found	nsubj
2	found	find	VERB	Mood=Ind Number=Sing Person=3 Tense=Past VerbForm=Fin	root	root
3	a	a	DET	Definite=Ind PronType=Art	4 counterexample	det
4	counterexample	counterexample	NOUN	Number=Sing	2 found	obj
5	and	and	CCONJ	_	6 won	cc
6	won	win	VERB	Mood=Ind Number=Sing Person=3 Tense=Past VerbForm=Fin	2 found	conj
7	the	the	DET	Definite=Def PronType=Art	8 argument	det
8	argument	argument	NOUN	Number=Sing	6 won	obj
9	.	.	PUNCT	_	2 found	punct

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	find	past	She	a counterexample					vn discover-84 «NP V NP»: agent=Agent counterexample=Topic
2	win	past	She not said here	the argument					vn succeed-74-2 «NP V NP»: agent=Agent argument=Eventuality

Example 6

Find a counterexample: All numbers ending in 9 are prime. (Answer: 9 itself.)

Sentence 1: Find a counterexample: All numbers ending in 9 are prime.

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	Find	find	VERB	Mood=Imp VerbForm=Fin	root	root
2	a	a	DET	Definite=Ind PronType=Art	3 counterexample	det
3	counterexample	counterexample	NOUN	Number=Sing	1 Find	obj
4	:	:	PUNCT	_	6 numbers	punct
5	All	all	DET	PronType=Tot	6 numbers	det
6	numbers	number	NOUN	Number=Plur	11 prime	nsubj
7	ending	end	VERB	VerbForm=Ger	6 numbers	acl
8	in	in	ADP	_	9 9	case
9	9	9	NUM	NumForm=Digit NumType=Card	7 ending	obl
10	are	be	AUX	Mood=Ind Number=Plur Person=3 Tense=Pres VerbForm=Fin	11 prime	cop
11	prime	prime	ADJ	Degree=Pos	1 Find	ccomp
12	.	.	PUNCT	_	1 Find	punct

#	verb	tense, mood	who	what, whom	where	other	roles by
1	find	imperative	you not said here	a counterexample			vn discover-84 «NP V NP»: agent=Agent counterexample=Topic
2	end	gerund	all numbers not said here		9		vn stop-55.4-1-1 «NP.eventuality V»: agent=Eventuality
3	is	present	all numbers			prime property	tree rules

Sentence 2: (Answer: 9 itself.)

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	(	(	PUNCT	_	2 Answer	punct
2	Answer	answer	NOUN	Number=Sing	root	root
3	:	:	PUNCT	_	4 9	punct
4	9	9	NUM	NumForm=Digit NumType=Card	2 Answer	appos
5	itself	itself	PRON	Case=Acc Gender=Neut Number=Sing Person=3 PronType=Emp Reflex=Yes	4 9	nmod
6	.	.	PUNCT	_	2 Answer	punct
7	)	)	PUNCT	_	2 Answer	punct

The frames reader finds no event or fact in this sentence.

Text: the school dictionary of Mova's schools (world/data/dictionary-schools/), written for Mova. Trees: Mova's own parse — the en model on the CPU, when the site is built — not checked by a teacher; they may be wrong. Frames: Mova's frames reader (prag), each meaning and example read on its own. Elamur Cosmic License.

This page in Markdown → https://md.mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/