Proposition: If a card has an even value on one side, then its opposite face is red.
The cards which MUST be turned over to verify the above proposition are
Understanding the Logic Proposition
The core task is to verify the conditional statement: "If a card has an even value on one side, then its opposite face is red." This follows the logical structure "If P, then Q", where:
- P represents "The card has an even value."
- Q represents "The opposite face is red."
To verify "If P, then Q", we must check cases that could potentially prove it false. A conditional statement is only false if P is true and Q is false.
Analyzing Visible Card Faces
We examine each of the four visible faces (2, 3, red, blue) to see if turning the card is necessary:
- Card showing '2': This card has an even value (P is true). To check if the proposition holds, we must verify that its opposite face is red (Q is true). If the opposite face is not red, the proposition is falsified. Therefore, this card must be turned.
- Card showing '3': This card has an odd value (P is false). The proposition "If P, then Q" makes no claims about what happens when P is false. Whether the other side is red or not, the proposition remains true. Therefore, this card does not need to be turned.
- Card showing 'red': This card shows a red face (Q is true). The proposition is "If even, then red". It does not imply the converse ("If red, then even"). A red card could have an odd number on its reverse side without violating the rule. Therefore, this card does not need to be turned.
- Card showing 'blue': This card shows a blue face (Q is false). If the hidden side of this card has an even value (P is true), it would directly contradict the proposition (P is true, but Q is false). We must turn this card to ensure its other side is not an even number. Therefore, this card must be turned.
Conclusion for Verification
To verify the proposition, we need to check the card that could represent the case "P is true" (the '2' card) and the card that could represent the case "Q is false" (the 'blue' card).
The cards that must be turned over are those showing '2' and 'blue'.
Important Questions from Logical Deduction
- The following observation is made about the scores obtained by 100 students in an exam:
'For each student, there exists another student in the class such that their scores are at most ten marks away.'
If the above statement is false, which one of the following statements is necessarily true? - Consider the following two phonological rules:
Rule 1: Vowel Epenthesis of [ɪ] after sibilant-ending stems
Rule 2: Progressive Voicing Assimilation of the plural affix
Which ONE of the following rule ordering relations apply in the case of regular English pluralization as in ‘horse’ – ‘horses’? Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
- Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
- Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
- The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______
- Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:
$P < Q$
$S > P > T$
$R < T$
If integers 1 through 5 are used to construct such a number, the value of P is:
