This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the visible questions: Question 1: Set Union Given P = \3, 5, 6\ and Q = \1, 2, 4\. Find P Q. Step 1: Identify the elements in set P and set Q. P = \3, 5, 6\ Q = \1, 2, 4\ Step 2: Combine all unique elements from both sets to form the union. The union P Q includes all elements that are in P or in Q (or both). P Q = \1, 2, 3, 4, 5, 6\ This corresponds to option A. The final answer is A. \1, 2, 3, 4, 5, 6\. Question 2: Logical Statement Let p be "You can go away". Let q be "You love yourself". Use a logical notation to describe the statement "If you go away then you love yourself". Step 1: Identify the propositions p and q. p: "You can go away" q: "You love yourself" Step 2: Translate the conditional statement "If ... then ..." into logical notation. The phrase "If A then B" is represented by A B. Therefore, "If you go away then you love yourself" is represented by p q. This corresponds to option C. The final answer is C. p q. Question 3: Probability A die is rolled once. What is the probability of obtaining a 2 or a 5? Step 1: Determine the sample space and total number of outcomes. When a fair die is rolled once, the possible outcomes are \1, 2, 3, 4, 5, 6\. The total number of outcomes is 6. Step 2: Identify the favorable outcomes. The event is "obtaining a 2 or a 5". The favorable outcomes are \2, 5\. The number of favorable outcomes is 2. Step 3: Calculate the probability. The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes. P(2 or 5) = Number of favorable outcomesTotal number of outcomes = (2)/(6) Step 4: Simplify the probability. P(2 or 5) = (1)/(3) The final answer is (1)/(3). Note on other questions: Question 7 (Truth Table): The last column of the truth table is not visible in the image, which is necessary to determine which logical expression matches it. Therefore, this question cannot be answered. Question 8 (Logarithm): The question "If _x y = 1.5, ..." is incomplete, so it cannot be solved. Send me the next one 📸