1 . To find the sets  X  and  Y  based on the given information, we need to interpret the provided conditions step by step.  ### Given:  1.  X ∪ Y = { 1 , 2 , 3 , 5 , 6 , 8 , 9 , 10 }  2.  X ∩ Y = { 1 , 5 }  3.  Y − X = { 2 , 6 , 9 , 10 } ### Step 1: Using  Y − X From condition 3, we know that: Y − X = { 2 , 6 , 9 , 10 }  This means that the elements  2 , 6 , 9 ,  and  10  are in  Y  but not in  X . Therefore, we can express  Y  as: Y = ( Y − X ) ∪ ( X ∩ Y )  Since  X ∩ Y = { 1 , 5 } , we can write: Y = { 2 , 6 , 9 , 10 } ∪ { 1 , 5 } = { 1 , 2 , 5 , 6 , 9 , 10 } ### Step 2: Using  X ∪ Y Now, we know: X ∪ Y = { 1 , 2 , 3 , 5 , 6 , 8 , 9 , 10 }  And we have  Y = { 1 , 2 , 5 , 6 , 9 , 10 } . Now we can find  X : X = ( X ∪ Y ) − Y  This gives us: X = { 1 , 2 , 3 , 5 , 6 , 8 , 9 , 10 } − { 1 , 2 , 5 , 6 , 9 , 10 }  Calculating this, we get: X = { 3 , 8 } ### Step 3: Verification  Now we need to verify if the derived sets satisfy all the conditions.  - **Checking  X ∪ Y **: X ∪ Y = { 3 , 8 } ∪ { 1 , 2 , 5 , 6 , 9 , 10 } = { 1 , 2 , 3 , 5 , 6 , 8 , 9 , 10 } (True) - **Checking  X ∩ Y **: X ∩ Y = { 3 , 8 } ∩ { 1 , 2 , 5 , 6 , 9 , 10 } = { 1 , 5 } (True) - **Checking  Y − X **: Y − X = { 1 , 2 , 5 , 6 , 9 , 10 } − { 3 , 8 } = { 2 , 6 , 9 , 10 } (True) ### Conclusion  Thus, the sets  X  and  Y  are:  X = { 3 , 8 }  Y = { 1 , 2 , 5 , 6 , 9 , 10 }

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Answer: Option False

Explanation: