How Logical are You?

Logic. What is it? Philosophy? Mathematics? Or something else? Do not confuse reasons which sound good with good, sound reasons. Can you tell those apart?

When presented with a Rubik's Cube, would you be able to solve it? Can you see faults in philosophical reasoning? Never mind all that. The question is: are you logical?

Created by: Zao
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1. In a competition, all entrants may pick any number between 1 and 100: the entry that is closest to two thirds of the mean shall win. Which of the following would you pick?
67.3
87
100
44.9
1
pi
2. On a desk are the cards: A, J, 3 and 8, with either a number or letter on the reverse side. You are given the rule: 'If a cards has a vowel on one side, then it has an even number on the other side.' To judge the correctness of the rule, which of the above cards would you turn over?
A, J and 3
J and 3
A and 3
A and 8
J and 8
A, J and 8
3. Which two of the following statements are logically equivalent? i)If A and B are both true, then C is true. ii)If A or B is false, then C is true. iii)If C is false, then A and B are both false. iv)If A and B are both false, then C is true.
A and B
A and C
A and D
B and C
B and D
C and D
4. Which of the following negates this statement:'All horses are fast'?
All horses are not fast
There exists a horse that is slow
No horse is fast
All horses are slow
Horses are of different speeds
All horses are not slow
5. Is the following a statement? This statement is false.
Yes, because it states something
No, because it contradicts itself
Yes, because it is a fact
No, because it is an opinion
Yes, because the statement is false
Insufficient information
6. There are three statements, A, B and C. What is equivalent to A implies (B implies C), otherwise written as A=> (B=>C)?
A (B C)
(B => A) => C
not (not B and not C) => A
not A => not (B=>C)
(C=> B) => A
(B and not C) => not A
7. Which is the odd one out?
There exists x such that for all y, ( P(y) = P(x))
There exists unique x such that P (x) is true
There exists P(x) and for all y,z, ((P(y) and P(z)) => y=z)
There exists and x such that ( P(x) and for all y, (P(y) => y=x))
There exists x so that for all y, P(y) is true if and only if y=x
8. Prime Minister John Major famously said that: 'If it isn't hurting, it isn't working'. What is wrong with this statement logically?
It means that anything that hurts, works
It is politically incorrect
A prime minister should feel for his country
It means that anything that doesn't hurt doesn't work
It means that John Major wants to cause hurt to his country by carrying out his policies
There is nothing wrong with the logic
9. Aaron and Bert have quarrelled, and decided to settle their differences by a duel to the death, using bazookas.At the beginning, they are 600m apart, and walk towards each other at the same speed. One hit is sufficient to kill, and that the chances of hitting increases linearly as the distance decreases. Each bazook is armed only with one round. Aaron know that Bert is 100% more accurate than he is - when should he open fire?
Don't bother
At 400m away
When Bert is next to him
At 200m away
At 600m away
At 10m away
10. A card game is played only with the cards J, Q, and K. You have only one opponent, and the higher card wins. You are dealt a Q, and are to act first; your opponent has already automatically put £1 into the pool. You should:
Snap fold all the time
Raise a third of the time, fold the rest
Call all the time
Raise all the time
Raise a third of the time, fold a third, and call a third.
Fold half the time, raise half the time.
11. A certain gameshow consists of a contestant picking randomly one out of three mystery boxes, with two being empty and one having £200 inside. The host then takes away a box with no prize in it, then the contestant has the chance to switch or keep the box he already has. If he switches and wins, he would have to pay a £50 fee, which goes to charity. Should he switch or not?
Yes, because that is the point of the game
No, because he might regret it if he did
Yes, because it improves his chances of winning
No, because it makes no difference to his chances of winning
Yes, because the fee goes to charity
No, because he has to pay the £50 fee

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