Consider the following statement about real numbers.
"Whichever positive number
When this statement is written in the formal language of proof, which of the following is obtained?
Proof, EXT2 P1 2020 HSC 8 MC
Consider the statement:
'If
Which of the following is the negation of this statement?
is odd and is not a multiple of 3 or 6. is even and is a multiple of 3 but not a multiple of 6. - If
is even, then is not a multiple of 3 and is not a multiple of 6. - If
is odd, then if is not a multiple of 3 then is not a multiple of 6.
Proof, EXT2 P1 2020 HSC 7 MC
Consider the proposition:
'If
Given that each of the following statements is true, which statement disproves the proposition?
is prime is divisible by 9 is prime is divisible by 23
Proof, EXT2 P1 SM-Bank 5 MC
Four cards are placed on a table with a letter on one face and a shape on the other.
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You are given the rule: "if N is on a card then a circle is on the other side."
Which cards need to be turned over to check if this rule holds?
- N and G
- G and triangle
- circle and N
- N and triangle
Proof, EXT2 P1 SM-Bank 1 MC
Consider the following statement.
"If you have no treasure, I have no kingdom."
Which of the following is logically equivalent to this statement?
- If I have no kingdom then you have no treasure.
- If you have treasure then I have a kingdom.
- If you have no kingdom then I have no treasure.
- If I have a kingdom then you have treasure.