This is a little bit off topic, but I think a good time to bring it up:
LC 31 says the covenant of grace was made with the "elect." But we believe in a mixed covenant in this world as well as a perfect covenant, right (Jer 31)? So if the covenant of grace was always made with the "elect" only, from Genesis 3 to Christ, are non-elect children still considered being in covenant with God? If so, how, if the covenant is truly only between God and the elect? Is the administration just different on this side of eternity? Thanks.
Not off topic. It's actually refreshing to deal with a genuine question.
Christ is set forth as the Mediator of the Covenant of Grace and, as Mediator, executes the offices of Prophet, Priest, and King.
The Church of Jesus Christ is the visible Kingdom of God and consists of those who have made profession of him as well as their Covenant children.
In this visible Kingdom, the Church, the Lord's Prophetic office is exhibited in the ministers of the Word who proclaim the Gospel as the Spirit, sent by the Father and the Son, works through the Word to convict and convert. The Lord's Kingly office is exhibited visibly by Church discipline and the binding and loosing.
Thus, the historical reality of the Covenant and the ingathering of the elect is accomplished through the Church's ministry of Word, Sacrament, and Discipline. The sacrament of baptism demarcks those who are in the visible Kingdom of God but the Spirit sovreignly confers the graces of the sign signfied to the elect through the Word. Thus, it can be said that all baptized members are visible members of the Kingdom of Christ but not all are united to Him by faith even though Word and Sacrament are means to that end.