. For n € N, Σ±1 (2k + 1) = n? + 2n.

Please solve and show work.

Suppose that the given statements are true. Find the other true statements. (a) Given: If the window is above the door, then Austin's cousin is a girl. Which statement must also be true? - If Austin's cousin is a girl, then the window is above the door. - If Austin's cousin is not a girl, then the window is not above the door. - If the window is not above the door, then Austin's cousin is not a girl. (b) Given: If the bike is fast, then Rachel sleeps on the floor. The bike is fast. Which statement must also be true? - The bike is not fast. - Rachel sleeps on the floor. - Rachel does not sleep on the floor. (c) Given: If David knows how to dance, then the tires are old. If the tires are old, then my favorite movie is being shown. Which statement must also be true? - If my favorite movie is being shown, then the tires are old. - If David knows how to dance, then my favorite movie is being shown. - If my favorite movie is being shown, then David knows how to…

Answer 2 and 3 in the question. Please make sure the answers are correct. This question is in three parts.  Given the premises: If the steak is well done, it’s overcooked. If the steak is overcooked, the fire alarm will go off. Either the batteries have been changed or the fire alarm will not go off. The batteries have only been changed if the ladder is in the room. The ladder is not in the room. Conclude that the steak is not well done. 2. These premises don’t make sense in the real world.  Why? 3. How can you change the premises so that they make sense in the real world?