Each one of the following conclusions has been made by child

Each one of the following conclusions has been made by children and adults. For which ones can you find a counterexample? (Select all that apply.) If you triple any number and add 1, the resulting number is always an odd number. If you double any number and add 1, the resulting number is always an odd number. If a number is divisible by 2 and by 3, then it is divisible by 6. If a figure has four right angles, then it must be a rectangle. If you square a number, you get an even number.

Solution

The conclusion that “If you triple any number and add 1, the resulting number is always an odd number” is FALSE. For example, 3*3 = 9 and 3*3+1 = 10, which is an even number. The conclusion that “If you double any number and add 1, the resulting number is always an odd number” is TRUE. the double of any number n, whether even or odd, positive or negative, is an even number 2n ( it is divisible by 2). If 1 is added to 2n, the resulting number 2n+1 will always be an odd number as it is not divisible by 2. The conclusion that “If a number is divisible by 2 and by 3, then it is divisible by 6” is TRUE. If 2 and 3 are factors of any number, then 2*3 will always be a factor of this number. The conclusion that “If a figure has four right angles, then it must be a rectangle” is technically TRUE as the figure can also be a square, but a square is also a rectangle. Both the pairs of opposite sides are congruent and also, both the pairs of opposite sides are parallel in any figure which has four right angles. The conclusion that “If you square a number, you get an even number” is FALSE as 32 = 9 and 9 is not an even number.