P=s r t , so, s= P/(st)
19999555
If a is rational then there exist integers p and q such that a = p/q where q>0. Similarly, b = r/s for some integers r and s (s>0) Then a*b = p/q * r/s = (p*r)/(q*s) Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0 Thus a*b can be expressed as x/y where p and r are integers implies that x = p*r is an integer q and s are positive integers implies that y = q*s is a positive integer. That is, a*b is rational.
Prove: [ P -> Q AND R -> S AND (P OR R) ] -> (Q OR S) -> NOT, --- 1. P -> Q ___ hypothesis 2. R -> S ___ hypothesis 3. P OR R ___ hypothesis 4. ~P OR Q ___ implication from hyp 1. 5. ~R OR S ___ implication from hyp 2 6. ~P OR Q OR S ___ addition to 4. 7. ~R OR Q OR S ___ addition to 5. 8. Let T == (Q OR S) ___ substitution 9. (~P OR T) AND (~R OR T) ___ Conjunction 6,7 10. T OR (~P AND ~R) ___ Distribution from 9 11. T OR ~(P OR R) ___ De Morgan's theorem 12. Let M == (P OR R) ___ substitution 13. (T OR ~M) AND M ___ conjunction 11, hyp 3 From there, you can use distribution to get (T AND M) OR (~M AND M). The contradiction goes away leaving you with T AND M, which can simplify to T.
500
500 Sheets of Paper in a Ream
500 Sheets in a Ream of Paper
it is the s&p 500
(S)tandard & (P)oor's 500. The S&P 500 is a market value weighted index of 500 blue-chip stocks, considered to be a benchmark of the overall stock market. If the S&P 500 is up, usually the market as a whole is also up.
the s means standard and the p is poor. the s and p 500 was to see who had a standard amount of something, the poor people could not use this.
P=s r t , so, s= P/(st)
p/q * r/s = (p*r)/(q*s)
19999555
A rational number is a number of the form p/q where p and q are integers and q > 0.If p/q and r/s are two rational numbers thenp/q + r/s = (p*s + q*r) / (q*r)andp/q - r/s = (p*s - q*r) / (q*r)The answers may need simplification.
500 Sheets in a Ream (of paper)
500 Sheets of Paper in a Ream
Om Jai Jagdish Hare s s s ss n s r Swami Jai Jagadeesh Hare r g m p p dp m g mr Bhakt Jano Ke Sankat rg r g m m g rs s Kshan Mein Door Kare s s r r gr s n sd Om Jai Jagadish Hare r r r r grs n s Jo Dhyawe Phal Pave rs s s rs s s rss Dukh Vinshe Man Ka p d p mg r s r Swami Dukh Vinshe Man Ka p p p d p mg r s r Sukh Sampati Ghar Aave r g r gm m m g grs Kasht Mite Tan Ka s r r r gr s n d Om Jai Jagdeesh Hare r r r rgr s n s Maat Pita Tum Mere rs s s rs s s rss Sharan Gahun Kiskee p d p m g r sr Swami Sharan Gahun Kiskee p p p d p m g r sr Tum Bin Aur Na Duja r g r g m m g grs Aas Karun Jiskee srr r gr s nd Om Jay Jagadish Hare r r r r grs n s Vishay Vikaar Mitao r s s s rs s s rss Paap Haro Deva pd p m g rsr swami Paap Haro Deva p p pd p m g rsr Shraddha Bhakti Badaao r g r g m m g grs Santan Ki Sewa s r r gr snd Om Jay Jagadish Hare r r r r grs n s Tan Man Dhan Sab Hai Tera r s s s r s s s s nsr Swami Sab Kuch Hai Tera p p p d p m g rsr Tera Tujhko Arpan rgrg m m m grs n Kya Lage Mera s r gr snd Om Jai Jagdeesh Hare r r r rgr s n s