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- https://math.libretexts.org/Bookshelves/Precalculus/Trigonometry_(Yoshiwara)/02%3A_Trigonometric_Ratios/2.00%3A_Side_and_Angle_RelationshipsIt is also true that the sum of the lengths of any two sides of a triangle must be greater than the third side, or else the two sides will not meet to form a triangle. In a right triangle, if c st...It is also true that the sum of the lengths of any two sides of a triangle must be greater than the third side, or else the two sides will not meet to form a triangle. In a right triangle, if c stands for the length of the hypotenuse, and the lengths of the two legs are denoted by a and b, then The figure shows a triangle inscribed in a unit circle, one side lying on the diameter of the circle and the opposite vertex at point (p,q) on the circle.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/06%3A_The_Converse_and_the_ContrapositiveThis page covers the concepts of converses and contrapositives in logic, explaining their significance and truth values. It highlights that the converse may not be true while the contrapositive is log...This page covers the concepts of converses and contrapositives in logic, explaining their significance and truth values. It highlights that the converse may not be true while the contrapositive is logically equivalent to the original statement. Examples clarify common misconceptions, and exercises are provided for practice. It discusses logical implications, specifically p→q, its converse, and contrapositive while addressing logical errors.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Professor_Holz'_Topics_in_Contemporary_Mathematics/01%3A_Logic/1.03%3A_Advanced_Truth_TablesBecause complex Boolean statements can get tricky to think about, we can create a truth table to keep track of what truth values for the simple statements make the complex statement true and false. A ...Because complex Boolean statements can get tricky to think about, we can create a truth table to keep track of what truth values for the simple statements make the complex statement true and false. A truth table shows what the resulting truth value of a complex statement is for all the possible truth values for simple statements.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/02%3A_Logic_and_Quantifiers/2.02%3A_ImplicationSuppose a mother makes the following statement to her child: “If you finish your peas, you’ll get dessert.” This is a compound sentence made up of the two simpler sentences P = “You finish your pea...Suppose a mother makes the following statement to her child: “If you finish your peas, you’ll get dessert.” This is a compound sentence made up of the two simpler sentences P = “You finish your peas” and D = “You’ll get dessert.” It is an example of a type of compound sentence called a conditional. Conditionals are if-then type statements. In ordinary language the word “then” is often elided (as is the case with our example above).
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/04%3A_Logic/4.03%3A_Truth_TablesBecause complex Boolean statements can get tricky to think about, we can create a truth table to keep track of what truth values for the simple statements make the complex statement true and false. A ...Because complex Boolean statements can get tricky to think about, we can create a truth table to keep track of what truth values for the simple statements make the complex statement true and false. A truth table shows what the resulting truth value of a complex statement is for all the possible truth values for simple statements.
