Let ${\mathbf{y}}_{\mathbf{1}}$and${\mathbf{y}}_{\mathbf{2}}$be two functions defined on$\mathbf{(}\mathbf{-}\infty \mathbf{,}\infty \mathbf{)}$.

1. True or False: If${\mathbf{y}}_{\mathbf{1}}$and${\mathbf{y}}_{\mathbf{2}}$are linearly dependent on the interval$\left[a,b\right]$, then${\mathbf{y}}_{\mathbf{1}}$and${\mathbf{y}}_{\mathbf{2}}$are linearly dependent on the smaller interval$\mathbf{[}\mathbf{c}\mathbf{,}\mathbf{d}\mathbf{]}\subset \mathbf{[}\mathbf{a}\mathbf{,}\mathbf{b}\mathbf{]}$.
2. True or False: If${\mathbf{y}}_{\mathbf{1}}$and${\mathbf{y}}_{\mathbf{2}}$are linearly dependent on the interval$\left[\mathbf{a}\mathbf{,}\mathbf{b}\right]$, then${\mathbf{y}}_{\mathbf{1}}$and${\mathbf{y}}_{\mathbf{2}}$are linearly dependent on the larger interval$\mathbf{[}\mathbf{C}\mathbf{,}\mathbf{D}\mathbf{]}\supset \mathbf{[}\mathbf{a}\mathbf{,}\mathbf{b}\mathbf{]}$.

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