The product of two numbers \(a\) and \(b\) is greater than \(100\). Prove that at least one of the numbers is greater than \(10\).
What is the contrapositive of the statement “If my car won’t start, then the battery is flat or there is no fuel”?
What is the contrapositive of the statement: ”If the temperature is above \(40^\circ\), then it is hot and sunny."
Some lines are drawn on a large sheet of paper so that all of them meet at one point. Show that if there are at least \(10\) lines, then there must be two lines whose angle between them is at most \(18^\circ\).
A whole number \(n\) has the property that when you multiply it by \(3\) and then add \(2\), the result is odd. Use a proof by contrapositive to show that \(n\) itself must be odd.