# Areas and logarithms (Topics in mathematics) by a i markushevich

By a i markushevich

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The standard form is: p→q q→r ∴p→r ∴q 14. First premise Second premise Conclusion (p ∧ ~q) ∧ (~p → q) p ~q T T F T F T F T T T F T F F F F F F F T The premises are true in row 2. Because the conclusion is true and the premises are both true, the argument is valid. p q 15. First premise Second premise Third premise Conclusion r p → ~r ~p → q p ∧q T T T T F T T T T F F T T T T F T T F T F T F F F T T F F T T T T T F F T F F T T F F F T T T F F F F F F T F F The premises are true in row 5. Because the conclusion is false and the premises are true, we know the argument is invalid.

So, T = 1, S = 5, and O = 0. Assume O = 1, since the sum of two single digits plus a carry of at most 1 is 19 or less. In the third column from the left, the two 1’s result in an S. Then S can be either 2 or 3. But since the right column also results in an S, and the two A’s are identical digits, S must be even, so S cannot be 3. Assume S = 2. Since A cannot equal 1, since O = 1, assume A = 6. Plants P Beautiful Flowers 5. The argument is valid. Mariachi R Baseball Rockers 1 C1C 6 7. The argument is valid.

Because the conclusion in row 3 is false and the premises are both true, we know the argument is invalid. h r 27. In symbolic form: ~b→d bVd ∴b First Second Conclusion premise premise b ~b→d b∨ d T T T T T T F T T T F T T T F F F F F F The premises are true in rows 1, 2, and 3. Because the conclusion in row 3 is false and the premises are both true, we know the argument is invalid. b d 29. In symbolic form: c→t t ∴c First Second Conclusion c premise premise t c→ t T T T T T T F F F T F T T T F F F T F F The premises are true in rows 1 and 3.