91Ó°ÊÓ

Expand each. $$\sum_{j=1}^{2} \sum_{i=1}^{3} a_{i j}$$

(Easter Sunday) The date for Easter Sunday in any year \(y\) can be computed as follows. Let \(a=y \bmod 19, b=y \bmod 4, c=y \bmod 7, d=(19 a+24)\) \(\bmod 30, e=(2 b+4 c+6 d+5) \bmod 7,\) and \(r=(22+d+e) .\) If \(r \leq 31,\) then Easter Sunday is March \(r ;\) otherwise, it is April \([r(\bmod 31)] .\) Compute the date for Easter Sunday in each year. $$2000$$

Rewrite each linear system as a matrix equation \(A X=B\). $$\begin{aligned} x-2 y &=4 \\ 3 x+y-z &=-5 \\ x+2 y-3 z &=6 \end{aligned}$$

Let \(f: X \rightarrow Y\) and \(g: Y \rightarrow Z\) be invertible functions. Prove each. $$\left(f^{-1}\right)^{-1}=f$$

Prove. If \(\Sigma\) is a finite alphabet, then \(\Sigma^{*}\) is countable.

Expand each. $$\sum_{1 \leq i

Let \(f: X \rightarrow Y\) and \(g: Y \rightarrow Z\) be invertible functions. Prove each. $$(g \circ f)^{-1}=f^{-1} \circ g^{-1}$$

(Easter Sunday) The date for Easter Sunday in any year \(y\) can be computed as follows. Let \(a=y \bmod 19, b=y \bmod 4, c=y \bmod 7, d=(19 a+24)\) \(\bmod 30, e=(2 b+4 c+6 d+5) \bmod 7,\) and \(r=(22+d+e) .\) If \(r \leq 31,\) then Easter Sunday is March \(r ;\) otherwise, it is April \([r(\bmod 31)] .\) Compute the date for Easter Sunday in each year. $$2076$$

Prove each. If \(\Sigma\) is a finite alphabet, then \(\Sigma^{*}\) is countable.

The date for Easter Sunday in any year \(y\) can be computed as follows. Let \(a=y \bmod 19, b=y \bmod 4, c=y \bmod 7, d=(19 a+24)\) \(\bmod 30, e=(2 b+4 c+6 d+5) \bmod 7,\) and \(r=(22+d+e) .\) If \(r \leq 31,\) then Easter Sunday is March \(r ;\) otherwise, it is April \([r(\bmod 31)] .\) Compute the date for Easter Sunday in each year. $$2076$$