From the course: Programming Foundations: Discrete Mathematics

Unlock the full course today

Join today to access over 24,900 courses taught by industry experts.

Prove logical equivalence

Prove logical equivalence

From the course: Programming Foundations: Discrete Mathematics

Start my 1-month free trial Buy for my team

Prove logical equivalence

“

- Logical equivalences. Although two statements might have very different semantic meaning, such as, dogs bark and cats meow, this can actually be logically equivalent to, the sky is blue and the grass is green. At first, this might sound absurd. But the reality is that both statements, on either side of the and operator, are true. So the overall statement is true. And if the overall statements match, in this case, both true, then they are considered logically equivalent. Using p and q to denote two separate statements, if they are logically equivalent, we can use this special symbol. P is logically equivalent to q. Remember, the semantic meaning of the sentence is not in question. Only the logical form of the statements. Truth tables are used to determine logical equivalence. By using the canonical form, we can easily determine if the conclusions match, without reordering the rows. To prove that two statement forms are not logically equivalent, we only need to find one row that is…

Contents