Wisdom Stacks

The Contrapositive: An Interactive Guide Unlock a fundamental concept in logic and math. What is a Contrapositive? In logic, every conditional statement of the form "If P, then Q" has a special partner called the contrapositive . The most important thing to remember is that a statement and its contrapositive are logically equivalent — if one is true, the other is guaranteed to be true as well. A conditional statement has two parts: the hypothesis (P) and the conclusion (Q) . To get the contrapositive, you simply swap the hypothesis and conclusion, and then negate both of them. Original Statement P → Q "If P, then Q" ...

2021-01 If the perimeter of a rectangle is 160 cm and its length is 50 cm, then its diagonal is \(50\) cm \(10\sqrt{34}\) cm \(40\) cm \(10\sqrt{41}\) cm \(30\) cm Solution Find the width of the rectangle: The perimeter of a rectangle is given by the formula \(P=2(l+w)\), where \(l\) is the length and \(w\) is the width. Given \(P=160\) cm and \(l=50\) cm. Substitute the values into the formula: \(160=2(50+w)\). Divide both sides by 2: \(80=50+w\). Subtract 50 from both sides: \(w=30\) cm. Calculate the diagonal using the Pythagorean theorem: The diagonal of a rectangle forms a right-angled triangle with the length and width as the other two sides. Using the Pythagorean theorem, \(d^{2}=l^{2}+w^{2}\)...