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Question
Verify if the following proposition is valid using the truth table:
(X ∧ Y) =>Z = (Y => Z) ∧ (X => Y).
Solution
| X | Y | Z | X ∧ Y | (X ∧ Y)=>Z | Y=>Z | X=>Y | (Y=>Z )∧(X=>Y) |
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
INVALID
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A shopping mall allows customers to shop using the cash or credit card of any nationalised bank. In awards bonus points to their customers on the basis of criteria given below:
- The customer is an employee of the shopping mall and makes the payment using a credit card.
OR - The customer shops items which carry bonus points and makes the payment using a credit card with a shopping amount of less than ₹10,000.
OR - The customer is not an employee of the shopping mall and makes the payment not through a credit card in cash for the shopping amount above ₹10,000/-
The inputs are:
| INPUTS | |
| C | Payment through a credit card. |
| A | Shopping amount in above ₹10,000 |
| E | The customer is an employee of the shopping mall. |
| I | Item carries a bonus point. |
(In all the above cases, 1 indicates yes and 0 indicates no.)
Output: X[1 indicates bonus point awarded, 0 indicates bonus point not awarded for all cases]
Draw the truth table for the inputs and outputs given above and write the POS expression for X(C, A, F, I).
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(A ☉ B)' = A ⊕ B
From the given logic diagram:
- Derive Boolean expression and draw the truth table for the derived expression
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