Prove or disprove the statements below.

(a) For all positive real numbers x and y, ⌊x ⋅ y⌋ ≤ ⌊x⌋ ⋅ ⌊y⌋.

(b) For all positive real numbers x and y, ⌈x ⋅ y⌉ ≤ ⌈x⌉ ⋅ ⌈y⌉.

please give the proof for if it is true or disprove I dont want the example

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