Do this [ Select ] ["Deductive", "Inductive", "Logical"] reasoning [ Select ] ["is", "is not"] useful when finding patterns and relies on the assumption that [ Select ] ["generalizations are wrong", "the pattern continues", "the proof works"] . However, [ Select ] ["deductive", "inductive"] reasoning can sometimes lead to a false conjecture. To show that a conjecture is false we must find [ Select ] ["one", "several", "two"] [ Select ] ["counterexample(s)", "example(s)", "explanation(s)", "solution(s)"] .

[ Select ] ["Deductive", "Inductive"] reasoning relies on proving that a conjecture is true in [ Select ] ["all", "at least one", "more than one", "one"] case(s). We do this by