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
- 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. In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of P, Q, and R ?
- Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.
Column-I Column-II P. This house is in a mess. 1. Alright, I won't bring it up during our conversations. Q. I am not happy with the marks given to me. 2. Well, you can easily look it up. R. Politics is a subject I avoid talking about. 3. No problem, let me clear it up for you. S. I don't know what this word means. 4. Don't worry, I will take it up with your teacher.
Identify the option that has the correct match between Column-I and Column-II. - In the following truth table, what does X stand for?
P Q X 1 1 1 1 0 0 0 1 0 0 0 1 A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K).
Which one of the following options displays the color codes that are consistent with the color model?
