The Mumford-Tate conjecture asserts that, via the Betti-étale comparison isomorphism, and for any smooth projective variety $ X $, over a number field $ K $, the $ \mathbb{Q}_{ \ell } $-linear combinations of Hodge cycles coincide with the $ \ell $-adic Tate cycles.

Question.Would that mean that if the Hodge conjecture and the Tate conjecture hold, then the Mumford-Tate conjecture holds as well ?