What differences exist between overlapping and disjoint restrictions?

Place the following symbols properly on the Stacked Diagram. Note: Write down the symbols ONLY. RQ P Z W N Shade the following boundaries that each item is requiring. Note: encircle the boundaries if they are INCLUDED or PART of what you are shading. 1. -5 0 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 4. -5 2x>5 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 5. x= 3 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 XYN'S MMW WORKTEXT

Circle correct choices from among Y, N, Proof, and Witness and provide below a proof or witness as the case may be: (lc) (1) Vx EN 3y €Z Y N Pf w Why? (ii) 3x EN Vy €Z Y N Pf W Why? (iii) Vx €N 3y € Z Y N Pf W Why? (vs) (iv) ax €Z vy €N Y N Pf W Why? (v) 3x €Z 3y € Z = 1 Y N PfW Why?

NOTE: blt is shorthand for “but less than: Value Categories: 100 blt 150; 150 blt 200; 200 blt 250; and 250 blt 300 Lot Size Categories: 0 blt 8; 8 blt 16; 16 blt 24; and 24 blt 32 Room Categories: 5; 6; 7; 8; 9; and 10 Age Categories: 14 blt 24; 24 blt 34; 34 blt 44; 44 blt 54; and 54 blt 64      QUESTIONS: 1. Is the population mean value of a house different from $175,000? Use alpha = 0.05. 2. Is the population proportion of the houses with modern kitchens greater than 0.60? Use alpha = 0.01. 3. Is there a relationship between the age of a house and whether or not a house has a fireplace? Use alpha = 0.05. 4. Are the proportions of houses within each value category equal? Use alpha = 0.05. 5. Is there a difference in the population average house values for houses with modern bathrooms and houses without modern bathrooms? Use alpha = 0.01.