Let t be a positive integer. Prove that 1 t C 2 t C 3 t C C n t can be written as a polynomial expression.
3.1 Logic Statement- a declarative sentence that is either true or false (but not both) Compound Statement- a declarative sentence compromised of two or more statements. These statements employ connectives (implicitly or explicitly) such as: and, but, or (Ex- I studied today and I will dance tonight.) Negation- a statement that implies or states the opposite of a given statement. (Ex- All Kutztown students study at least eight hours per week. The negation would be no Kutztown students studies eight hours, there is at least one.) And and but statements are conjuctions. Or statements are a disjunction. Not statements are a negation. A conjunction is only true when both components are true. 3.2 Truth Tables Negation of an existential is a universally quantified statement and vice versa. Ex: There is a featherless bird. (existential) Negation: All birds have feathers. (universal) Statements are logically equivalent if the last columns of their truth tables are identical. Tautology- a statement that is always true.