Q-2: [4+4 marks ] a) Define A△B=(A−B)∪(B−A) , where A,B are any two sets. Show that (AΔB)ΔC=AΔ(BΔC) b) Prove or disprove: i. ⌈x⌉=−⌊x⌋ . ii. For all positive real numbers x and y,⌊x⋅y⌋≤⌊x⌋⋅⌊y⌋ .

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