Four institutes, $\text{A, B, C,}$ and $\text{D}$, had contracts with four vendors $\text{W, X, Y,}$ and $\text{Z}$ during the ten calendar years from $2010$ to $2019$. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes.
The following facts are also known about these contracts.
- Vendor $\text{Z}$ had at least one contract in every year.
- Vendor $\text{X}$ had one or more contracts in every year up to $2015$, but no contract in any year after that.
- Vendor $\text{Y}$ had contracts in $2010$ and $2019$. Vendor $\text{W}$ had contracts only in $2012$.
- There were five contracts in $2012$.
- There were exactly four multi-year contracts. Institute $\text{B}$ had a $7$-year contract, $\text{D}$ had a $4$-year contract, and $\text{A}$ and $\text{C}$ had one $3-$year contract each. The other four contracts were single$-$year contracts.
- Institute $\text{C}$ had one or more contracts in $2012$ but did not have any contract in $2011$.
- Institutes $\text{B}$ and $\text{D}$ each had exactly one contract in $2012$. Institute $\text{D}$ did not have any contract in $2010$.
Which of the following is true?
- $\text{D}$ had a contract with $\text{Y}$ in $2019$
- $\text{D}$ had a contract with $\text{X}$ in $2011$
- $\text{B}$ had a contract with $\text{Y}$ in $2019$
- $\text{B}$ had a contract with $\text{Z}$ in $2017$