If-Then Statements

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Show your work for each problem.

1.
What is the hypothesis of the statement "If it rains, then the football match is cancelled"?
1. a)It rains
2. b)The football match is cancelled
3. c)The match is not cancelled
4. d)It does not rain
2.
Complete the conditional so that it is true: if $x = 4$ , then $3x - 2 = \square$ . Which number goes in the box?
3.
Check the conditional "If $x = 6$ , then $2x + 3 = 15$ " by computing $2x + 3$ for $x = 6$ .
4.
Which sentence is "All squares are rectangles" written in if-then form?
1. a)If a shape has four sides, then it is a square
2. b)If a shape is a rectangle, then it is a square
3. c)If a shape is a square, then it is a rectangle
4. d)If a shape is not a square, then it is not a rectangle
5.
The truth table of $p \to q$ has 4 rows. In how many of these rows is $p \to q$ false?
6.
A shop's rule: if your order is at least 30 dollars, then delivery is free. You buy a book for 12 dollars and a game for 15 dollars. How many dollars more must you spend so that delivery is free?
7.
In which case is the conditional $p \to q$ false?
1. a) $p$ false, $q$ true
2. b) $p$ true, $q$ false
3. c) $p$ true, $q$ true
4. d) $p$ false, $q$ false
8.
The statement "If a whole number is greater than 5, then it is greater than 8" is false. What is the smallest whole number that is a counterexample?
9.
Claim: if a whole number is divisible by 2, then it is divisible by 4. Find the smallest positive counterexample.
10.
Mia says: "If I finish my homework, then I go to the cinema." She did not finish her homework, but she went to the cinema anyway. Is her statement true or false?
1. a)We cannot say, because the hypothesis is false
2. b)False, because she did not finish her homework
3. c)True, because the hypothesis is false, so the promise is not broken
4. d)False, because she went to the cinema
11.
A shop's rule: if you buy at least 3 notebooks, then each notebook costs 2 dollars instead of 3 dollars. You buy 4 notebooks. How many dollars do you pay in total?
12.
Statement: if a number is a multiple of 6, then it is a multiple of 3. Check the statement for the number 42: first divide 42 by 6, then by 3. What is $42 \div 3$ ?
13.
Rule: if the temperature is below 18 °C, then the heating turns on. At 7:00 the room is 23 °C, and the temperature drops by 2 °C every hour. After how many full hours does the heating turn on for the first time?
14.
Which number is a counterexample to the statement "If a number is prime, then it is odd"?
1. a)3
2. b)2
3. c)15
4. d)9
15.
Claim: if $n$ is a whole number greater than 1, then $n^2 + n + 1$ is prime. What is the smallest counterexample $n$ ?
16.
Claim: if $n$ is a positive whole number, then $2^n + 1$ is prime. Test $n = 1, 2, 3$ and find the smallest counterexample.
17.
Statement: if $x > 2$ , then $x^2 > 9$ . Which of the whole numbers 3, 4 and 5 is a counterexample?
18.
Four cards each have a number on one side and a color on the other. You see: 4, 7, red, blue. Rule: if a card has an even number on one side, then its other side is red. Which cards must you turn over to check the rule, and how many are they?