Conjecture: All shapes have 3 sides.
FALSE
Counterexample: square
Conjecture:
a*1=a
TRUE, by the identity property of multiplication.
Conjecture: The only football team in Texas is the Dallas Cowboys.
FALSE
counterexamples: Houston Texans, HC knights, University of Texas Longhorns, etc.
Conjecture: Mr. Cohen does not root for any sports teams.
FALSE:
Counterexample: Mr. Cohen roots for Holy Cross sports teams, Iowa State sports teams, Notre Dame sports teams, and MN sports teams...
FALSE
Counterexample: Spiders have 8 legs
Conjecture: Parallel lines never intersect.
TRUE, by definition of a parallel
Conjecture: If x^2≥9, then x must equal 3.
FALSE
Counterexample: x = 4 or 5 or 6 or ...
FALSE:
Counterexamples: Quarterback, Running Back, Offensive Line, Kicker, etc.
Conjecture: Mr. Cohen recently graduated from college.
TRUE, Mr. Cohen graduated from Notre Dame this Spring/Summer.
Conjecture: There are no students at Holy Cross.
FALSE
Counterexample: Name any student.