integration of lnx 0 to 1 limit thanks me later

3 Bit Synchronous Up/Down counter using T Flip Flop | MOD 8 UP-Down Counter

yesma 15 samma jana parxa haina rw aani 11 dekhi 15 samma ma don't care hunxa aani k map farak banxa tara yt haru ma kasai ley 10 samma garey rw k map solve haneyko xan ( nepali youtuber (Entic nepal) tara indian youtuber ley chai 15 samma which one is right. 😭

Simplify the Boolean function F(P,Q,R,S) =Π(0,1,4,5,11,14,15) and d(P,Q,R,S) =Σ(2,3,7,8,9,13) using K-Map in both SOP and POS form.

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