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
Step 1: Understand the given sets. We are given two sets: Y = \house, tree\ V = \cat, house, tree\ Step 2: Analyze the relationship between the sets. We need to determine which statement is true. • For Y = V to be true, both sets must contain exactly the same elements. Y has "house" and "tree", while V has "cat", "house", and "tree". Since V contains "cat" which is not in Y, Y ≠ V. So, option A is false. • For Y V (Y is a proper subset of V) to be true, every element of Y must also be an element of V, and V must contain at least one element not in Y. The elements of Y are "house" and "tree". Both "house" and "tree" are present in V. The set V contains "cat", which is not in Y. Therefore, Y is a proper subset of V. So, option B is true. • For V Y (V is a proper subset of Y) to be true, every element of V must also be an element of Y, and Y must contain at least one element not in V. The element "cat" is in V but not in Y. Therefore, V is not a subset of Y. So, option C is false. • For V Y (V is an element of Y) to be true, the entire set V must be one of the items listed inside the curly braces of Y. The elements of Y are "house" and "tree", not the set V. So, option D is false. Step 3: Conclude the correct statement. Based on the analysis, the statement Y V is true. The correct option is B. B. Y V That's 2 down. 3 left today — send the next one.